Black Hole Collisions

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Black Hole Collisions Black Hole Collisions Frans Pretorius Frans Pretorius Princeton University Princeton University Inaugural Conference of Inaugural Conference of the Institute for the Institute for Gravitation and the Gravitation and the Cosmos Cosmos August 9, 2007 August 9, 2007

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Black Hole Collisions. Frans Pretorius Princeton University Inaugural Conference of the Institute for Gravitation and the Cosmos August 9, 2007. Outline. Motivation: why explore black hole collisions? Anatomy of a merger - PowerPoint PPT Presentation

Transcript of Black Hole Collisions

Page 1: Black Hole Collisions

Black Hole CollisionsBlack Hole Collisions

Frans PretoriusFrans PretoriusPrinceton UniversityPrinceton University

Inaugural Conference of the Inaugural Conference of the Institute for Gravitation and Institute for Gravitation and

the Cosmosthe Cosmos

August 9, 2007August 9, 2007

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OutlineOutline• Motivation: why explore black hole collisions?Motivation: why explore black hole collisions?

• Anatomy of a mergerAnatomy of a merger

– overview of the stages of a merger : “Newtonian”, inspiral, overview of the stages of a merger : “Newtonian”, inspiral, plunge/merger, ringdownplunge/merger, ringdown

• Recent results Recent results

– numerical solution of the field equationsnumerical solution of the field equations

– look at a couple of highlightslook at a couple of highlights• remarkable simplicity of the waveform, in particular briefness (non-existence?) remarkable simplicity of the waveform, in particular briefness (non-existence?)

of a “plunge”of a “plunge”• large kick velocitieslarge kick velocities

• Beyond astrophysical binariesBeyond astrophysical binaries

– zoom-whirl like behavior at an “immediate threshold” of mergerzoom-whirl like behavior at an “immediate threshold” of merger

– speculations about ultrarelativistic collisions, and possible applications in speculations about ultrarelativistic collisions, and possible applications in high energy particle experimentshigh energy particle experiments

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Motivation: why explore black hole Motivation: why explore black hole collisions?collisions?

• gravitational wave astronomygravitational wave astronomy

– almost overwhelming evidence that black holes exist in our universe, and when almost overwhelming evidence that black holes exist in our universe, and when they merge we expect them to be strong sources of gravitational wavesthey merge we expect them to be strong sources of gravitational waves

– understanding the nature of the waves emitted in the process is important for understanding the nature of the waves emitted in the process is important for detecting such events, and moreover will be detecting such events, and moreover will be crucialcrucial in deciphering the signals in deciphering the signals

• extracting the parameters of the binaryextracting the parameters of the binary

• obtain clues about the environment of the binaryobtain clues about the environment of the binary

• how accurately does Einstein’s theory describe the event?how accurately does Einstein’s theory describe the event?

– a black hole is not “merely” a strong gravitational field, but a region in which spacetime itself is a black hole is not “merely” a strong gravitational field, but a region in which spacetime itself is undergoing undergoing gravitational collapsegravitational collapse, a truly remarkable concept wholly outside the realm of any , a truly remarkable concept wholly outside the realm of any present tests of general relativitypresent tests of general relativity

• understanding general relativityunderstanding general relativity

– if general relativity is the correct theory of “gravity”, we certainly want to fully if general relativity is the correct theory of “gravity”, we certainly want to fully understand one of the most fundamental interactions in nature … the two body understand one of the most fundamental interactions in nature … the two body problemproblem

– black hole collisions, in particular in the ultrarelativistic regime, offer an intuitive black hole collisions, in particular in the ultrarelativistic regime, offer an intuitive route to explore the highly dynamical, non-linear regime of the theory route to explore the highly dynamical, non-linear regime of the theory

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Anatomy of a MergerAnatomy of a Merger• In the conventional scenario of a black hole merger in the universe, one In the conventional scenario of a black hole merger in the universe, one

can break down the evolution into 4 stages: can break down the evolution into 4 stages: Newtonian, inspiral, Newtonian, inspiral, plunge/merger and ringdownplunge/merger and ringdown

• NewtonianNewtonian

– in isolation, radiation reaction will cause two black holes of mass in isolation, radiation reaction will cause two black holes of mass MM in a in a circular orbit with initial separation circular orbit with initial separation RR to merge within a time to merge within a time ttmm relative to the relative to the Hubble time Hubble time ttHH

– label the phase of the orbit label the phase of the orbit Newtonian Newtonian when the separation is such that the when the separation is such that the binary will take longer than the age of the universe to merge, for then to be of binary will take longer than the age of the universe to merge, for then to be of relevance to gravitational wave detection, other “Newtonian” processes need relevance to gravitational wave detection, other “Newtonian” processes need to operate, e.g. dynamical friction, n-body encounters, gas-drag, etc. For e.g., to operate, e.g. dynamical friction, n-body encounters, gas-drag, etc. For e.g.,

• two solar mass black holes need to be within 1 million Schwarzschild radii ~ 3 million two solar mass black holes need to be within 1 million Schwarzschild radii ~ 3 million kmkm

• two 10two 1099 solar mass black holes need to be within 6 thousand Schwarzschild radii ~ 1 solar mass black holes need to be within 6 thousand Schwarzschild radii ~ 1

parsecparsec

4

610

sH

m

RR

MM

tt

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Anatomy of a MergerAnatomy of a Merger• inspiralinspiral

– In the inspiral phase, energy loss through gravitational wave emission In the inspiral phase, energy loss through gravitational wave emission is the dominate mechanism forcing the black holes closer togetheris the dominate mechanism forcing the black holes closer together

– to get an idea for the inspiral time scale, for equal mass, circular to get an idea for the inspiral time scale, for equal mass, circular binaries the Keplarian orbital frequency offers a good approximation binaries the Keplarian orbital frequency offers a good approximation until very close to merger until very close to merger

– Post-Newtonian techniques provide an accurate description of the Post-Newtonian techniques provide an accurate description of the process until remarkably close to mergerprocess until remarkably close to merger

• though being an expansion in though being an expansion in v/cv/c, that near merger the black hole velocities , that near merger the black hole velocities “only” reach “only” reach v~0.3cv~0.3c, and that the state-of-the-art has certain aspects of the , and that the state-of-the-art has certain aspects of the dynamics computed to dynamics computed to (v/c)(v/c)77, it is perhaps not that surprising in hind-sight, it is perhaps not that surprising in hind-sight

2/3

3 kHz1121

2

RR

MM

RM s

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Anatomy of a MergerAnatomy of a Merger• plunge/mergerplunge/merger

– this is the time in the merger when the two event horizons this is the time in the merger when the two event horizons coalesce into one (viewed as an evolution with respect to some coalesce into one (viewed as an evolution with respect to some well-behaved time slice)well-behaved time slice)

• we know the two black holes we know the two black holes mustmust merge into one if cosmic merge into one if cosmic censorship holds (and no indications of a failure yet in any merger censorship holds (and no indications of a failure yet in any merger simulations)simulations)

– full numerical solution of the field equations are required to solve full numerical solution of the field equations are required to solve for the geometry of spacetime in this stage for the geometry of spacetime in this stage

– in all cases studied to date, this stage is exceedingly short, in all cases studied to date, this stage is exceedingly short, leaving its imprint in on the order of 1-2 gravitational wave cycles leaving its imprint in on the order of 1-2 gravitational wave cycles at roughly twice the final orbital frequencyat roughly twice the final orbital frequency

MM

sRR

kHz112

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Anatomy of a MergerAnatomy of a Merger• ringdownringdown

– in the final phase of the merger, the remnant black hole “looses all its in the final phase of the merger, the remnant black hole “looses all its hair”, settling down to a Kerr black holehair”, settling down to a Kerr black hole

– one possible definition for when plunge/merger ends and ringdown begins, one possible definition for when plunge/merger ends and ringdown begins, is when the spacetime can adequately be described as a Kerr black hole is when the spacetime can adequately be described as a Kerr black hole perturbed by a set of perturbed by a set of quasi-normal modes (QNM)quasi-normal modes (QNM)

– the ringdown portion of the waveform will be dominated by the the ringdown portion of the waveform will be dominated by the fundamental harmonic of the quadrupole QNM, with characteristic fundamental harmonic of the quadrupole QNM, with characteristic frequency and decay time frequency and decay time [Echeverria, PRD 34, 384 (1986)]:[Echeverria, PRD 34, 384 (1986)]:

j=a/Mj=a/Mf f , the Kerr spin parameter of the black hole , the Kerr spin parameter of the black hole

3.0

45.0

3.0

163.01120

)1(63.01kHz322

jj

MMs

jM

M

QNM

QNM

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Sample evolution --- Cook-Sample evolution --- Cook-Pfeiffer Quasi-circular Initial dataPfeiffer Quasi-circular Initial data

This animation shows the This animation shows the lapse functionlapse function in the orbital in the orbital plane.plane.

The lapse function The lapse function represents the relative time represents the relative time dilation between a dilation between a hypothetical observer at the hypothetical observer at the given location on the grid, given location on the grid, and an observer situated and an observer situated very far from the system --- very far from the system --- the redder the color, the the redder the color, the slower local clocks are slower local clocks are running relative to clocks at running relative to clocks at infinityinfinity

If this were in “real-time” it If this were in “real-time” it would correspond to the would correspond to the merger of two ~5000 solar merger of two ~5000 solar mass black holesmass black holes

Initial black holes are close Initial black holes are close to non-spinning to non-spinning Schwarzschild black holes; Schwarzschild black holes; final black hole is a Kerr a final black hole is a Kerr a black hole with spin black hole with spin parameter parameter ~0.7, ~0.7, and ~and ~4%4% of the of the total initial rest-mass of the system total initial rest-mass of the system is emitted in gravitational wavesis emitted in gravitational waves

A. Buonanno, G.B. Cook and F.P.; A. Buonanno, G.B. Cook and F.P.; Phys.Rev.D75:124018,2007Phys.Rev.D75:124018,2007

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Gravitational waves from the Gravitational waves from the simulationsimulation

A depiction of the gravitational A depiction of the gravitational waves emitted in the orbital waves emitted in the orbital plane of the binary. Shown is plane of the binary. Shown is the real component of the the real component of the Newman Penrose scalar Newman Penrose scalar , , which in the wave zone is which in the wave zone is proportional to the second time proportional to the second time derivative of the usual plus-derivative of the usual plus-polarizationpolarization

The plus-component of the wave The plus-component of the wave from the same simulation, from the same simulation, measured on the axis normal to measured on the axis normal to the orbital planethe orbital plane

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What does the merger wave represent? What does the merger wave represent? • Scale the system to two Scale the system to two 10 solar mass (~10 solar mass (~ 2x102x103131 kg) BHs kg) BHs

– radius of each black hole in the binary is ~ radius of each black hole in the binary is ~ 30km30km

– radius of final black hole is ~ radius of final black hole is ~ 60km60km

– distance from the final black hole where the wave was measured ~distance from the final black hole where the wave was measured ~ 1500km 1500km

– frequency of the wave ~frequency of the wave ~ 200Hz (early inspiral) - 800Hz (ring-down) 200Hz (early inspiral) - 800Hz (ring-down)

– fractional oscillatory “distortion” in space induced by the wave transverse to fractional oscillatory “distortion” in space induced by the wave transverse to the direction of propagation has a the direction of propagation has a maximummaximum amplitude amplitude L/LL/L ~ 3x10~ 3x10-3-3

• a 2m tall person will get stretched/squeezed by ~ a 2m tall person will get stretched/squeezed by ~ 6 mm6 mm as the wave passes as the wave passes

• LIGO’s arm length would change by ~ LIGO’s arm length would change by ~ 12m12m. Wave amplitude decays like . Wave amplitude decays like 1/distance from source; e.g. at 10Mpc the change in arms ~ 1/distance from source; e.g. at 10Mpc the change in arms ~ 5x105x10-17-17m m (1/20 the (1/20 the radius of a proton, which is well within the ballpark of what LIGO is trying to radius of a proton, which is well within the ballpark of what LIGO is trying to measure!!)measure!!)

– despite the seemingly small amplitude for the wave, the energy it carries is despite the seemingly small amplitude for the wave, the energy it carries is enormous — around enormous — around 10103030 kg c kg c22 ~ 10 ~ 104747 J ~ 10 J ~ 105454 ergs ergs

• peak luminosity is about 1/100peak luminosity is about 1/100thth the Planck luminosity of 10 the Planck luminosity of 105959ergs/s !!ergs/s !!• luminosity of the sun ~ 10luminosity of the sun ~ 103333ergs/s, a bright supernova or milky-way type galaxy ~ ergs/s, a bright supernova or milky-way type galaxy ~

10104242 ergs/s ergs/s• if all the energy reaching LIGO from the 10Mpc event could directly be converted if all the energy reaching LIGO from the 10Mpc event could directly be converted

to sound waves, it would have an intensity level of ~ 80dBto sound waves, it would have an intensity level of ~ 80dB

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Numerical RelativityNumerical Relativity• Numerical relativity is concerned with solving the field equations of general Numerical relativity is concerned with solving the field equations of general

relativityrelativity

using computers. using computers.

• When written in terms of the spacetime metric, defined by the usual line elementWhen written in terms of the spacetime metric, defined by the usual line element

the field equations form a the field equations form a system of 10 coupled, non-linear, second order partial system of 10 coupled, non-linear, second order partial differential equations, each depending on the 4 spacetime coordinatesdifferential equations, each depending on the 4 spacetime coordinates

– it is this system of equations that we need to solve for the 10 metric elements (plus it is this system of equations that we need to solve for the 10 metric elements (plus whatever matter we want to couple to gravity)whatever matter we want to couple to gravity)

– for many problems this has turned out to be quite an undertaking, due in part to the for many problems this has turned out to be quite an undertaking, due in part to the mathematical complexity of the equations, and also the heavy computational resources mathematical complexity of the equations, and also the heavy computational resources required to solve themrequired to solve them

• The field equations may be complicated, but they are The field equations may be complicated, but they are thethe equations that we believe equations that we believe govern the structure of space and time (barring quantum effects and ignoring govern the structure of space and time (barring quantum effects and ignoring matter). That they can, in principle, be solved in many “real-universe” scenarios is matter). That they can, in principle, be solved in many “real-universe” scenarios is a remarkable and unique situation in physics. a remarkable and unique situation in physics.

πTG 8

dxdxgds 2

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Minimal requirements for a formulation of the field equations Minimal requirements for a formulation of the field equations that that mightmight form the basis of a successful numerical integration form the basis of a successful numerical integration

schemescheme• Choose coordinates/system-of-variables that fix the character of the equationsChoose coordinates/system-of-variables that fix the character of the equations

– three common choicesthree common choices• free evolutionfree evolution — system of hyperbolic equations — system of hyperbolic equations• constrained evolutionconstrained evolution — system of hyperbolic and elliptic equations — system of hyperbolic and elliptic equations• characteristiccharacteristic or or null evolutionnull evolution — integration along the lightcones of the spacetime — integration along the lightcones of the spacetime

• For free evolution, need a system of equations that is well behaved off the For free evolution, need a system of equations that is well behaved off the ”constraint ”constraint manifold”manifold”

– analytically, if satisfied at the initial time the constraint equations of GR will be satisfied for all timeanalytically, if satisfied at the initial time the constraint equations of GR will be satisfied for all time

– numerically the constraints can only be satisfied to within the truncation error of the numerical numerically the constraints can only be satisfied to within the truncation error of the numerical scheme, hence we do not want a formulation that is “unstable” when the evolution proceeds slightly scheme, hence we do not want a formulation that is “unstable” when the evolution proceeds slightly off the constraint manifoldoff the constraint manifold

• Need well behaved coordinates (or gauges) that do not develop pathologies when the Need well behaved coordinates (or gauges) that do not develop pathologies when the spacetime is evolvedspacetime is evolved

– typically need dynamical coordinate conditions that can adapt to unfolding features of the spacetimetypically need dynamical coordinate conditions that can adapt to unfolding features of the spacetime

• Boundary conditions also historically a source of headaches Boundary conditions also historically a source of headaches

– naive BC’s don’t preserve the constraint nor are representative of the physicsnaive BC’s don’t preserve the constraint nor are representative of the physics– fancy BC’s can preserve the constraints, but again miss the physicsfancy BC’s can preserve the constraints, but again miss the physics– solution … compactify to infinity solution … compactify to infinity

• Geometric singularities in black hole spacetimes need to be dealt with: excision/punctures Geometric singularities in black hole spacetimes need to be dealt with: excision/punctures

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Computational issues in numerical solution of the Computational issues in numerical solution of the field equationsfield equations

• Each equation contains tens to hundreds of individual terms, requiring Each equation contains tens to hundreds of individual terms, requiring on the order of on the order of several thousand floating point operations several thousand floating point operations per grid point per grid point with any evolution scheme.with any evolution scheme.

• Problems of interest often have Problems of interest often have several orders of magnitude of relevant several orders of magnitude of relevant physical length scalesphysical length scales that need to be well resolved. In an equal mass that need to be well resolved. In an equal mass binary black hole merger for example:binary black hole merger for example:

• radius of each black hole radius of each black hole R~2MR~2M• orbital radius orbital radius ~ 20M (~ 20M (which is also the dominant wavelength of radiation emitted)which is also the dominant wavelength of radiation emitted)• outer boundary outer boundary ~ 200M~ 200M, as the waves must be measured in the weak-field regime , as the waves must be measured in the weak-field regime

to coincide with what detectors will seeto coincide with what detectors will see

– Can solve these problems with a combination of hardware technology — Can solve these problems with a combination of hardware technology — supercomputers — and software algorithms, in particular adaptive mesh supercomputers — and software algorithms, in particular adaptive mesh refinement (AMR)refinement (AMR)

• vast majority of numerical relativity codes today use finite difference techniques vast majority of numerical relativity codes today use finite difference techniques (predominantly 2(predominantly 2ndnd to 6 to 6thth order), notable exception is the Caltech/Cornell pseudo- order), notable exception is the Caltech/Cornell pseudo-spectral code spectral code

• How to deal with the true geometric singularities that exist inside all How to deal with the true geometric singularities that exist inside all black holes?black holes?

• excision, puncturesexcision, punctures

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Brief (and incomplete) history of the binary Brief (and incomplete) history of the binary black hole problem in numerical relativityblack hole problem in numerical relativity

• Hahn and Lindquist, Hahn and Lindquist, Ann. Phys. 19, 304 (1964)Ann. Phys. 19, 304 (1964) First simulation of “wormhole” initial data First simulation of “wormhole” initial data

• L. Smarr, L. Smarr, PhD Thesis (1977)PhD Thesis (1977) : First head-on collision simulation : First head-on collision simulation

• P. Anninos, D. Hobill, E.Seidel, L. Smarr, W. Suen P. Anninos, D. Hobill, E.Seidel, L. Smarr, W. Suen PRL 71, 2851 (1993)PRL 71, 2851 (1993) : Improved simulation : Improved simulation of head-on collisionof head-on collision

• B. Bruegmann B. Bruegmann Int. J. Mod. Phys. D8, 85 (1999)Int. J. Mod. Phys. D8, 85 (1999) : First grazing collision of two black holes : First grazing collision of two black holes

• mid 90’s-early 2000: Binary Black Hole Grand Challenge Alliancemid 90’s-early 2000: Binary Black Hole Grand Challenge Alliance– Cornell,PSU,Syracuse,UT Austin,U Pitt, UIUC,UNC, Wash. U, NWU … head-on collisions, grazing Cornell,PSU,Syracuse,UT Austin,U Pitt, UIUC,UNC, Wash. U, NWU … head-on collisions, grazing

collisions, cauchy-characteristic matching, singularity excisioncollisions, cauchy-characteristic matching, singularity excision

• B. Bruegmann, W. Tichy, N. Jansen B. Bruegmann, W. Tichy, N. Jansen PRL 92, 211101 (2004)PRL 92, 211101 (2004) : First full orbit of a quasi-circular : First full orbit of a quasi-circular binarybinary

• FP, FP, PRL 95, 121101 (2005)PRL 95, 121101 (2005) : First “complete” simulation of a non head-on merger event: : First “complete” simulation of a non head-on merger event: orbit, coalescence, ringdown and gravitational wave extractionorbit, coalescence, ringdown and gravitational wave extraction

• M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower PRL 96, 111101, (2006)PRL 96, 111101, (2006);; J. G. Baker, J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter J. Centrella, D. Choi, M. Koppitz, J. van Meter PRL 96, 111102, (2006)PRL 96, 111102, (2006) … several other groups … several other groups have now repeated these results: PSU, Jena, AEI, LSU, Caltech/Cornellhave now repeated these results: PSU, Jena, AEI, LSU, Caltech/Cornell

– note that to go from “a to b” here has required a tremendous amount of research in understanding the note that to go from “a to b” here has required a tremendous amount of research in understanding the mathematical structure of the field equations, stable discretization schemes, dealing with geometric mathematical structure of the field equations, stable discretization schemes, dealing with geometric singularities inside black holes, computational algorithms, initial data, extracting useful physical singularities inside black holes, computational algorithms, initial data, extracting useful physical information from simulations, etc. information from simulations, etc.

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Current state of the field Current state of the field • Two quite different, stable methods of integrating the Einstein field Two quite different, stable methods of integrating the Einstein field

equations for this problemequations for this problem

– generalized harmonic coordinates with constraint dampinggeneralized harmonic coordinates with constraint damping, , F.Pretorius, PRL F.Pretorius, PRL 95, 121101 (2005)95, 121101 (2005)

• Caltech/Cornell, Caltech/Cornell, L. Lindblom et al., Class.Quant.Grav. 23 (2006) S447-S462L. Lindblom et al., Class.Quant.Grav. 23 (2006) S447-S462

• PITT/AEI/LSU, PITT/AEI/LSU, B. Szilagyi et al., gr-qc/0612150B. Szilagyi et al., gr-qc/0612150

– BSSN with “moving punctures”,BSSN with “moving punctures”, M. Campanelli, C. O. Lousto, P. Marronetti, Y. M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower PRL 96, 111101, (2006); J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Zlochower PRL 96, 111101, (2006); J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter PRL 96, 111102, (2006)Meter PRL 96, 111102, (2006)

• Pennstate, Pennstate, F. Herrmann et al., gr-gc/0601026F. Herrmann et al., gr-gc/0601026

• Jena/FAU, Jena/FAU, J. A. Gonzalez et al., gr-gc/06010154J. A. Gonzalez et al., gr-gc/06010154

• LSU/AEI/UNAM, LSU/AEI/UNAM, J. Thornburg et al., gr-gc/0701038J. Thornburg et al., gr-gc/0701038

• U.Tokyo/UWM, U.Tokyo/UWM, M. Shibata et al, astro-ph/0611522M. Shibata et al, astro-ph/0611522

• U. Sperhake, gr-qc/0606079U. Sperhake, gr-qc/0606079

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• Many studies to date suggest the structure ofMany studies to date suggest the structure ofthe waveform is remarkably “simple”the waveform is remarkably “simple”

– most detailed examination of waveforms from non-most detailed examination of waveforms from non-spinning initial conditions, though qualitatively results spinning initial conditions, though qualitatively results seem to hold for more generic casesseem to hold for more generic cases

– ““quadrupole” physics seems to dominates GW quadrupole” physics seems to dominates GW emission; I.e. no strong signs of non-linear mode-emission; I.e. no strong signs of non-linear mode-coupling, intricacies in the inspiral portion of the wave coupling, intricacies in the inspiral portion of the wave structure come from orbital evolutionstructure come from orbital evolution

– merger/plunge phase short; in fact difficult to even merger/plunge phase short; in fact difficult to even identify a distinctive plungeidentify a distinctive plunge

Simplicity of the merger waveformSimplicity of the merger waveform

• Most useful consequence of the simple waveform structure is Most useful consequence of the simple waveform structure is that it that it seemsseems like it will be possible to construct fully analytical like it will be possible to construct fully analytical perturbative models of the waveforms, with numerical perturbative models of the waveforms, with numerical simulations supplying key matching parameterssimulations supplying key matching parameters

• Best example to date is from Best example to date is from A. Buonanno, Y.Pan, J. G. Baker, J. A. Buonanno, Y.Pan, J. G. Baker, J. Centrella, B. J. Kelly, S.T. McWilliams and J. R. van Meter, arXiv:0706.3732Centrella, B. J. Kelly, S.T. McWilliams and J. R. van Meter, arXiv:0706.3732 (figure to right showns 4:1 mass ratio example)(figure to right showns 4:1 mass ratio example)

• effective-one-body (EOB) PN inspiral connected to the 3 dominant QNMs, at effective-one-body (EOB) PN inspiral connected to the 3 dominant QNMs, at peak of resummed EOB frequencypeak of resummed EOB frequency

• added “pseudo” 4PN term to EOB model, with coefficient determined by a added “pseudo” 4PN term to EOB model, with coefficient determined by a best-fit match to a set of numerical resultsbest-fit match to a set of numerical results

• used simulation results for final spin and black hole mass to fix the QNM used simulation results for final spin and black hole mass to fix the QNM frequencies and decay constants frequencies and decay constants

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Results: Large recoil velocities in binary Results: Large recoil velocities in binary mergersmergers

• much excitement about the large kick velocities of upwards of 4000km/s seen in much excitement about the large kick velocities of upwards of 4000km/s seen in simulationssimulations [ [F. Herrmann et al., gr-qc/0701143; M. Koppitz et al., gr-qc/0701163; M. Campanelli et al. gr-F. Herrmann et al., gr-qc/0701143; M. Koppitz et al., gr-qc/0701163; M. Campanelli et al. gr-qc/0701164 & gr-qc/0702133, J.A. Gonzalez et al, arXiv:gr-qc/0702052, W. Tichy and P. Marronetti, arXiv:gr-qc/0701164 & gr-qc/0702133, J.A. Gonzalez et al, arXiv:gr-qc/0702052, W. Tichy and P. Marronetti, arXiv:gr-qc/0703075v1qc/0703075v1]]

• initial concern that this is an apparent contradiction with the observation that initial concern that this is an apparent contradiction with the observation that supermassive black holes are observed in the centers of most galaxies together supermassive black holes are observed in the centers of most galaxies together with the standard hierarchical structure formation scenario, howeverwith the standard hierarchical structure formation scenario, however

– uniform sampling over spin vector orientations and mass ratios for two a=.9 black holes uniform sampling over spin vector orientations and mass ratios for two a=.9 black holes with m1/m2 between 1 and 10 suggested only around 2% of parameter space has kicks with m1/m2 between 1 and 10 suggested only around 2% of parameter space has kicks larger than 1000km/s, and 10% larger than 500km/s [larger than 1000km/s, and 10% larger than 500km/s [J. Schnittman & A. Buonanno, J. Schnittman & A. Buonanno, astro-ph/0702641astro-ph/0702641]]

– astrophysical population is most likely highly non-uniform, e.g. torques astrophysical population is most likely highly non-uniform, e.g. torques from accreting gas in supermassive merger scenarios tend to align the spin from accreting gas in supermassive merger scenarios tend to align the spin and orbital angular momenta, which will result in more modest kick and orbital angular momenta, which will result in more modest kick velocities <~200km/s [velocities <~200km/s [T.Bogdanovic et al, astro-ph/0703054T.Bogdanovic et al, astro-ph/0703054] ]

– a couple of studies so far looking at 1) growth of supermassive black holes from a couple of studies so far looking at 1) growth of supermassive black holes from intermediate mass seeds [intermediate mass seeds [M.Micic, T. Abel and S. Sigurdsson, astro-ph/0512123M.Micic, T. Abel and S. Sigurdsson, astro-ph/0512123] and 2) following ] and 2) following the growth of black holes through a simplified merger tree model [the growth of black holes through a simplified merger tree model [ J. Schnittman, J. Schnittman, arXiv:0706.1548arXiv:0706.1548] found that the presence of supermassive black holes in most galactic ] found that the presence of supermassive black holes in most galactic centers is rather robust even if large kick velocities are assumedcenters is rather robust even if large kick velocities are assumed

• recent in-depth explanations of this [recent in-depth explanations of this [B. Bruegmann et al., arXiv:0707.0135v1,B. Bruegmann et al., arXiv:0707.0135v1, J. Schnittman et al., J. Schnittman et al., arXiv:0707.0301v1arXiv:0707.0301v1]]

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Large recoil velocities in binary mergersLarge recoil velocities in binary mergers

• scenario giving rise to very large kick velocities is, at scenario giving rise to very large kick velocities is, at a first glance, quite bizarre: a first glance, quite bizarre:

– equal masses with equal but opposite spin vectors equal masses with equal but opposite spin vectors in the orbital planein the orbital plane

– kick direction is normal to the orbital plane, but kick direction is normal to the orbital plane, but magnitude depends sinusoidally on the initial magnitude depends sinusoidally on the initial phasephase

– is linearly dependent on the magnitude of the spinis linearly dependent on the magnitude of the spin

– still “small” from a dimensional analysis point of still “small” from a dimensional analysis point of view, but enormous in an astrophysical settingview, but enormous in an astrophysical setting

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Frame dragging induced kicksFrame dragging induced kicks

• Can intuitively understand this phenomena Can intuitively understand this phenomena as a as a frame dragging effectframe dragging effect

– think of BH 1 (2) moving in the background think of BH 1 (2) moving in the background space time of BH 2 (1)space time of BH 2 (1)

– relative to BH 1 (2)’s spin vector, BH 2 (1) relative to BH 1 (2)’s spin vector, BH 2 (1) has zero orbital angular momentum … has zero orbital angular momentum … such a “particle” in a BH background is such a “particle” in a BH background is dragged by the rotation of the BH with a dragged by the rotation of the BH with a velocity velocity

v ~ 2 m a sin(v ~ 2 m a sin() / r) / r22

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Frame dragging induced kicksFrame dragging induced kicks• The result of this in the equal mass problem with the The result of this in the equal mass problem with the

particular configuration for maximum kicks is that the particular configuration for maximum kicks is that the entire orbital planeentire orbital plane will oscillate sinusoidally in the will oscillate sinusoidally in the direction normal to the orbital plane with the orbital direction normal to the orbital plane with the orbital frequency, and maximum velocity of frequency, and maximum velocity of 2 m a / r2 m a / r22

• The binary is emitting gravitational radiation, with the The binary is emitting gravitational radiation, with the largest flux normal to the orbital plane … the frame largest flux normal to the orbital plane … the frame dragging induced oscillations will cause a periodic dragging induced oscillations will cause a periodic doppler shift of the radiation along the axis, alternating doppler shift of the radiation along the axis, alternating between red and blue shift in one direction with the between red and blue shift in one direction with the opposite in the otheropposite in the other

• Averaged over an orbit, and without inspiral, the net Averaged over an orbit, and without inspiral, the net momentum radiated is zero. However, the merger event momentum radiated is zero. However, the merger event stops this process, and depending on where it’s stopped stops this process, and depending on where it’s stopped there will be linear momentum radiated normal to the there will be linear momentum radiated normal to the orbital plane … to conserve momentum the final black orbital plane … to conserve momentum the final black hole is given a kick in the opposite direction hole is given a kick in the opposite direction

Page 23: Black Hole Collisions

Frame dragging induced kicksFrame dragging induced kicks

• To estimate the maximum kick:To estimate the maximum kick:

– assume radiation stops once the black hole assume radiation stops once the black hole separation is within separation is within r~2M (M=2m)r~2M (M=2m)

– energy of a gravitational wave ~ frequency-squared energy of a gravitational wave ~ frequency-squared … doppler shift by maximum frame dragging velocity … doppler shift by maximum frame dragging velocity at at rr

– let the net energy radiated over the last ½ orbit be let the net energy radiated over the last ½ orbit be MM, then:, then:

vvrecoilrecoil ~ ~ (a/m)/2(a/m)/2

– with typical with typical ~ 1-2%, ~ 1-2%, get get vvrecoilrecoil ~ (a/m) 1500-3000 km/s ~ (a/m) 1500-3000 km/s

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Frame-dragging induced kicksFrame-dragging induced kicks• this seems to be consistent with what’s happening in this seems to be consistent with what’s happening in

simulationssimulations– however, none of this is gauge invariant, so take this in the same however, none of this is gauge invariant, so take this in the same

spirit as the order-of-magnitude calculation spirit as the order-of-magnitude calculation

equal mass merger, “scattering” initial conditions with impact parameter equal mass merger, “scattering” initial conditions with impact parameter ~14m, initial velocities ~0.12 in +- y direction, initial spins a/m=0.5 anti-~14m, initial velocities ~0.12 in +- y direction, initial spins a/m=0.5 anti-aligned in +- x direction aligned in +- x direction

Page 25: Black Hole Collisions

The threshold of immediate mergerThe threshold of immediate merger

• Consider the black hole scattering problemConsider the black hole scattering problem

• in general two, distinctin general two, distinct end-states possibleend-states possible

• one black hole, after a collisionone black hole, after a collision

• two isolated black holes, after a deflectiontwo isolated black holes, after a deflection

• because there are because there are two distinct end-statestwo distinct end-states, there must be some , there must be some kind of threshold behavior approaching a critical impact kind of threshold behavior approaching a critical impact parameter parameter b*b*

bbmm11,v,v11

mm22,v,v22

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The threshold of immediate mergerThe threshold of immediate merger• The following illustrates what could happen as one tunes to threshold, The following illustrates what could happen as one tunes to threshold,

assuming smooth dependence of the trajectories as a function of assuming smooth dependence of the trajectories as a function of b b

• non-spinning case (so we have evolution in a plane)non-spinning case (so we have evolution in a plane)

• only showing one of the BH trajectories for clarity only showing one of the BH trajectories for clarity

• solid blue (black) – merger (escape)solid blue (black) – merger (escape)

• dashed blue (black) – merger (escape) for values of dashed blue (black) – merger (escape) for values of bb closer to threshold closer to threshold

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The immediate threshold in the geodesic limit for The immediate threshold in the geodesic limit for equatorial orbits equatorial orbits

work with work with D. Khurana, D. Khurana,

gr-qc/0702084 gr-qc/0702084

• Here, regardless of the initial conditions (as long as we have an interpolating family), Here, regardless of the initial conditions (as long as we have an interpolating family), near threshold the geodesic enters a phase where it orbits arbitrarily close to near threshold the geodesic enters a phase where it orbits arbitrarily close to one of the one of the unstable circular geodesics of the spacetimeunstable circular geodesics of the spacetime

– about a Schwarzschild BH circular orbits become unstable in the rangeabout a Schwarzschild BH circular orbits become unstable in the range r=1.5Rr=1.5Rss (the “light ring”) (the “light ring”) toto r=3Rr=3Rss (the ISCO - innermost stable circular orbit)(the ISCO - innermost stable circular orbit)

– the number of orbits spent in the near-circular configuration scales as the number of orbits spent in the near-circular configuration scales as

wherewhere, with , with the orbital frequency and the orbital frequency and the Lyapunov exponent of the unstable the Lyapunov exponent of the unstable orbitorbit

un-bound orbit un-bound orbit exampleexample

bound orbit bound orbit example; the example; the threshold threshold solution is a solution is a homoclinic homoclinic orbitorbit

*bben

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The threshold of immediate merger for equal mass The threshold of immediate merger for equal mass black holesblack holes

work with work with D. Khurana, D. Khurana,

gr-qc/0702084 gr-qc/0702084

• In the equal mass problem the immediate threshold also exists, and In the equal mass problem the immediate threshold also exists, and remarkable exhibits remarkable exhibits quantitativelyquantitatively similar properties to the geodesic case similar properties to the geodesic case

– the primary difference is that in the circular phase the binary is emitting copious the primary difference is that in the circular phase the binary is emitting copious amounts of gravitational radiation (on the order of 1-1.5% per orbit)amounts of gravitational radiation (on the order of 1-1.5% per orbit)

– that the system is losing energy implies that the process cannot continue for ever, that the system is losing energy implies that the process cannot continue for ever, and will (probably) stop after all the excess kinetic energy of the orbit has been and will (probably) stop after all the excess kinetic energy of the orbit has been radiated away, which in the high-speed limit can be an arbitrary large fraction of the radiated away, which in the high-speed limit can be an arbitrary large fraction of the net energy of the spacetimenet energy of the spacetime

two cases tuned close to thresholdtwo cases tuned close to threshold(only 1 BH trajectory shown)(only 1 BH trajectory shown)

dominant component of emitted dominant component of emitted gravitational wavesgravitational waves

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Animations …Animations …

Lapse function Lapse function , orbital plane, orbital plane Real component of the Real component of the Newman-Penrose scalar Newman-Penrose scalar 44( times rM), orbital plane( times rM), orbital plane

Page 30: Black Hole Collisions

How quantitatively similar is the geodeosic and equal mass How quantitatively similar is the geodeosic and equal mass behavior? behavior?

• In the equal mass case there is no sensible notion of an unstable circular orbit, In the equal mass case there is no sensible notion of an unstable circular orbit, though we can still probe this regime by setting up a similar scattering though we can still probe this regime by setting up a similar scattering experiment and seeing whether the relationship between the impact experiment and seeing whether the relationship between the impact parameter and number of whirl-orbits holdparameter and number of whirl-orbits hold

• Indeed it does, and the scaling exponent is even close to an “analogous” Indeed it does, and the scaling exponent is even close to an “analogous” geodesic problem, considering a geodesic corotating about a black hole with geodesic problem, considering a geodesic corotating about a black hole with spin equal to the final spin of the merged object in the equal mass case (~0.7)spin equal to the final spin of the merged object in the equal mass case (~0.7)

Equal mass merger approach to immediate thresholdEqual mass merger approach to immediate threshold

Scaling exponents for Kerr equatorial geodesics (thin Scaling exponents for Kerr equatorial geodesics (thin dashed black lines from analytic perturbative calculation, dashed black lines from analytic perturbative calculation, colored lines from numerical integration of geodiscs; red colored lines from numerical integration of geodiscs; red ellipse is single “dot” from the equal mass case)ellipse is single “dot” from the equal mass case)

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How far can this go in the non-linear How far can this go in the non-linear case?case?

• System is losing energy, and quite rapidly, so there must be a limit to the System is losing energy, and quite rapidly, so there must be a limit to the number of orbits we can getnumber of orbits we can get

• Hawking’s area theoremHawking’s area theorem: assume cosmic censorship and “reasonable” forms : assume cosmic censorship and “reasonable” forms of matter, then net area of all black holes in the universe can of matter, then net area of all black holes in the universe can notnot decreasedecrease with timewith time

– the area of a single, isolated black hole is: the area of a single, isolated black hole is:

– initially, we have two non-rotating initially, we have two non-rotating (J=0)(J=0) black holes, each with mass black holes, each with mass M/2M/2::

– maximum energy that can be extracted from the system is if the final black hole is maximum energy that can be extracted from the system is if the final black hole is also non-rotating:also non-rotating:

in otherwords, the maximum energy that can be lost is a factor in otherwords, the maximum energy that can be lost is a factor 1-1/√2 ~ 29%1-1/√2 ~ 29%

– If the trend in the simulations continues, and the final If the trend in the simulations continues, and the final J~0.7MJ~0.7M22, we still get close to , we still get close to 24%24% energy that could be radiated energy that could be radiated

• the simulations show around 1-1.5% energy is lost per whirl, so we may get close to 15-30 the simulations show around 1-1.5% energy is lost per whirl, so we may get close to 15-30 orbits at the threshold of this fine-tuning process!orbits at the threshold of this fine-tuning process!

4

22 118

MJMA

22 816 MMA ff

28 MAi

Page 32: Black Hole Collisions

Can we go even further?Can we go even further?• What about the black hole scattering problem?What about the black hole scattering problem?

– give the black holes sizeable boosts, such that the net energy of the system is give the black holes sizeable boosts, such that the net energy of the system is dominated by the kinetic energy of the black holesdominated by the kinetic energy of the black holes

– set up initial conditions to have a one-parameter family of solutions that set up initial conditions to have a one-parameter family of solutions that smoothly interpolate between coalescence and scatter smoothly interpolate between coalescence and scatter

• ““natural” choice is the impact parameternatural” choice is the impact parameter

– it is it is plausibleplausible that at threshold, that at threshold, allall of the kinetic energy is converted to of the kinetic energy is converted to gravitational radiationgravitational radiation

• this can be an this can be an arbitrarily large fraction of the total energyarbitrarily large fraction of the total energy of the system (scale the rest of the system (scale the rest mass to zero as the boost goes to 1) mass to zero as the boost goes to 1)

• In the In the infiniteinfinite limit, taken so that the energy remains finite, each initial limit, taken so that the energy remains finite, each initial “black hole” is described by the Aichelburg-Sexl solution, which does not “black hole” is described by the Aichelburg-Sexl solution, which does not contain an event horizon. Thus, in this case the threshold of immediate contain an event horizon. Thus, in this case the threshold of immediate merger will also correspond to the merger will also correspond to the threshold of black hole formationthreshold of black hole formation

– If Choptuik’s hypothesis of universality at threshold holds, the threshold If Choptuik’s hypothesis of universality at threshold holds, the threshold ultrarelativistic black hole collision solution will (for a time) be given by the ultrarelativistic black hole collision solution will (for a time) be given by the Abrahams & Evans Brill wave critical collapse spacetimeAbrahams & Evans Brill wave critical collapse spacetime

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An application to the LHC?An application to the LHC?• The Large Hadron Collider (LHC) is a particle accelerator currently The Large Hadron Collider (LHC) is a particle accelerator currently

under construction near Lake Geneva, Switzerlandunder construction near Lake Geneva, Switzerland

– it will be able to collide beams of protons with center of mass it will be able to collide beams of protons with center of mass energies up to energies up to 14 TeV14 TeV

• In recent years the idea of In recent years the idea of large extra dimensionslarge extra dimensions have become have become popular [popular [N. Arkani-Hamed , S. Dimopoulos & G.R. Dvali, Phys.Lett.B429:263-272; L. Randall & R. N. Arkani-Hamed , S. Dimopoulos & G.R. Dvali, Phys.Lett.B429:263-272; L. Randall & R. Sundrum [Phys.Rev.Lett.83:3370-3373Sundrum [Phys.Rev.Lett.83:3370-3373]]

– we (ordinary particles) live on a 4-dimensional we (ordinary particles) live on a 4-dimensional branebrane of a higher of a higher dimensional spacetimedimensional spacetime

• ““large” extra dimensions are sub-mm in size, but large large” extra dimensions are sub-mm in size, but large compared to the 4D compared to the 4D Planck lengthPlanck length of of 1010-33-33 cm cm

– gravity propagates in all dimensionsgravity propagates in all dimensions

• The 4D The 4D Planck Energy,Planck Energy, where we expect quantum where we expect quantum gravity effects to become important, is gravity effects to become important, is 10101919 GeV GeV; ; however the presence of extra dimensions can change however the presence of extra dimensions can change the “true” Planck energy the “true” Planck energy

• A Planck scale in the TeV range is preferred as this A Planck scale in the TeV range is preferred as this solves the hierarchy problemsolves the hierarchy problem

• current experiments rule out Planck energies <~ current experiments rule out Planck energies <~ 1TeV1TeV

• Collisions of particles with super-Planck energies in Collisions of particles with super-Planck energies in these scenarios would cause black holes to be these scenarios would cause black holes to be produced at the LHC!produced at the LHC!

• can “detect” black holes via Hawking radiation or can “detect” black holes via Hawking radiation or missing energy missing energy

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The parton scattering problem The parton scattering problem • Consider the high speed collision of two partons with impact parameter Consider the high speed collision of two partons with impact parameter bb

– if the energy is beyond the Planck regime, to a good approximation this may look like a black if the energy is beyond the Planck regime, to a good approximation this may look like a black hole collisionhole collision

– for sufficiently high velocities charge and spin of the parton will be irrelevant (though both will for sufficiently high velocities charge and spin of the parton will be irrelevant (though both will probably be important at LHC energies) probably be important at LHC energies)

• if similar scaling behavior is seen as with geodesics and full simulations of the equal mass/low if similar scaling behavior is seen as with geodesics and full simulations of the equal mass/low velocity regime in general, can use the geodesic analogue to obtain an approximate idea of the cross velocity regime in general, can use the geodesic analogue to obtain an approximate idea of the cross section and energy loss to radiation vs. impact parameter … Ingredients:section and energy loss to radiation vs. impact parameter … Ingredients:

– map geodesic motion on a Kerr back ground with map geodesic motion on a Kerr back ground with (M,a)(M,a) to the scattering problem with total initial to the scattering problem with total initial energy energy E=ME=M and angular momentum and angular momentum aa of the black hole that’s formed near threshold of the black hole that’s formed near threshold

– find find andand b* b* using geodesic motionusing geodesic motion

– assume a constant fraction assume a constant fraction of the remaining energy of the system is radiated per orbit near of the remaining energy of the system is radiated per orbit near threshold (estimate using quadrupole formulathreshold (estimate using quadrupole formula))

– Integrate near-threshold scaling relation to find Integrate near-threshold scaling relation to find E(b)E(b) with the above parameters and the following with the above parameters and the following “boundary” conditions: “boundary” conditions: E(0), E(b*)E(0), E(b*) and and E(infinity)

• E(b*)E(b*) must be ~ 1 in kinetic energy dominated regime must be ~ 1 in kinetic energy dominated regime• E(infinity)=0E(infinity)=0• E(0)E(0) … need some other input, either perturbative calculations, or full numerical simulations. … need some other input, either perturbative calculations, or full numerical simulations.

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The parton scattering problem The parton scattering problem

• What value of the Kerr spin parameter to use?What value of the Kerr spin parameter to use?

– in the ultra-relativistic limit the geodesic asymptotes to the light-ring at thresholdin the ultra-relativistic limit the geodesic asymptotes to the light-ring at threshold

– it also seems “natural” that in this limit the final spin of the black hole at it also seems “natural” that in this limit the final spin of the black hole at threshold is threshold is a=1a=1. This is consistent with simple estimates of energy/angular . This is consistent with simple estimates of energy/angular momentum radiated momentum radiated

• quadrupole physics gives the following for the relative rates at which energy vs. angular quadrupole physics gives the following for the relative rates at which energy vs. angular momentum is radiated in a circular orbit with orbital frequency momentum is radiated in a circular orbit with orbital frequency ::

• for the scattering problem with the same impact parameter as a threshold geodesic on for the scattering problem with the same impact parameter as a threshold geodesic on an extremal Kerr background, the initial an extremal Kerr background, the initial J/EJ/E22=1=1. The Boyer-Lindquist value of . The Boyer-Lindquist value of EE is ½ for a is ½ for a geodesic on the light ring of an extremal Kerr BH, in that regime geodesic on the light ring of an extremal Kerr BH, in that regime d(J/ Ed(J/ E22)=0)=0

• But now we have a bit of a dilemma, as the extremal Kerr background has But now we have a bit of a dilemma, as the extremal Kerr background has no no unstableunstable circular geodesics, and hence circular geodesics, and hence tends to infinity in this limit tends to infinity in this limit

– will use will use aa close to but not exactly 1 to find out what close to but not exactly 1 to find out what E(b)E(b) might look like might look like

2

2

211)/(EJ

EdndE

EdnEJd

Page 36: Black Hole Collisions

Sample energy radiated vs. impact parameter curves Sample energy radiated vs. impact parameter curves (normalized) (normalized)

• An estimate of E(0) from An estimate of E(0) from Cardoso et al., Cardoso et al., Class.Quant.Grav. 22 (2005) L61-R84Class.Quant.Grav. 22 (2005) L61-R84

• Cross section for black hole formation Cross section for black hole formation (b<~1) would thus be (b<~1) would thus be 22EE22

• In higher dimensions for equatorial In higher dimensions for equatorial geodesics of Myers-Perry black holes geodesics of Myers-Perry black holes becomes quite small regardless of the becomes quite small regardless of the spin (spin (C. MerrickC. Merrick))

– probably related to the fact that there probably related to the fact that there are no are no stablestable circular geodesics for d>4 circular geodesics for d>4

– implies implies E(b)E(b) is well approximated by the is well approximated by the function, modulo the “spike” at function, modulo the “spike” at b=b*b=b*

• dE/dn ~ dE/dn ~ /40/40 in this limit, so expect all the in this limit, so expect all the energy to be radiated away in around a dozen energy to be radiated away in around a dozen orbits. orbits.

bbEbE *0~)(

Page 37: Black Hole Collisions

ConclusionsConclusions• the next few of decades are going to be a very exciting the next few of decades are going to be a very exciting

time for gravitational physicstime for gravitational physics

– numerical simulations are finally allowing us to fully reveal the numerical simulations are finally allowing us to fully reveal the fascinating landscape of binary coalescence within Einstein’s fascinating landscape of binary coalescence within Einstein’s theory of general relativity theory of general relativity

– gravitational wave detectors should allow us to see the gravitational wave detectors should allow us to see the universe in gravitational radiation for the first timeuniverse in gravitational radiation for the first time

– if extra dimensions exists, the next generation of high energy if extra dimensions exists, the next generation of high energy particle experiments might discover themparticle experiments might discover them

• black holes could therefore revolutionize our understanding black holes could therefore revolutionize our understanding of the universe from the smallest to largest scales!of the universe from the smallest to largest scales!

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ConclusionsConclusions• Why are the results in the “full, non-linear” regime so simple? Why are the results in the “full, non-linear” regime so simple?

– they’re not really … what the results are saying is that all the mathematical they’re not really … what the results are saying is that all the mathematical machinery developed over the years to study aspects of the two body problem machinery developed over the years to study aspects of the two body problem has, despite not having full solutions, uncovered much of the interesting has, despite not having full solutions, uncovered much of the interesting phenomonology:phenomonology:

• rich orbital motion (perihelion precession and zoom-whirl orbits, unstable orbits, rich orbital motion (perihelion precession and zoom-whirl orbits, unstable orbits, chaotic orbits, spin-spin and spin-obit precession, …) chaotic orbits, spin-spin and spin-obit precession, …)

• the “instability” of a binary to gravitational wave emissionthe “instability” of a binary to gravitational wave emission

• thethe end-state of the two body problem is a perturbed Kerr black hole, quickly ringing end-state of the two body problem is a perturbed Kerr black hole, quickly ringing down to the Kerr solutiondown to the Kerr solution

– any surprises yet to come? any surprises yet to come?

• probably not it in generic scenariosprobably not it in generic scenarios

• place to look would be in place to look would be in extremeextreme settings : settings : a a 1, 1,

– though if the last two years of results are any indication, the interesting gems will though if the last two years of results are any indication, the interesting gems will be contained in the work of Penrose, D’eath, Szekeres, … from the 60’s and 70’s!be contained in the work of Penrose, D’eath, Szekeres, … from the 60’s and 70’s!