Analogue Models For General Relativity

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Tim Lamberton and Dr Katrina Hibberd Centre for Mathematical Physics

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Analogue Models For General Relativity. Tim Lamberton and Dr Katrina Hibberd. Centre for Mathematical Physics. Talk Outline. Motivation Analogies provide new ways of looking at a problem . home.tiscali.nl. Talk Outline. An analogue model The “acoustic metric”. Motivation - PowerPoint PPT Presentation

Transcript of Analogue Models For General Relativity

Page 1: Analogue Models For  General Relativity

Tim Lamberton and Dr Katrina Hibberd

Centre for Mathematical Physics

Page 2: Analogue Models For  General Relativity

Talk Outline

home.tiscali.nl

● Motivation Analogies provide

new ways of looking at a problem

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Talk Outline

● An analogue model The “acoustic metric”

home.tiscali.nl

● Motivation Analogies provide

new ways of looking at a problem

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Talk Outline

● An analogue model The “acoustic metric”

● General relativity Metrics, black hole horizon, Hawking radiation

home.tiscali.nl

● Motivation Analogies provide

new ways of looking at a problem

Page 5: Analogue Models For  General Relativity

Talk Outline

● An analogue model The “acoustic metric”

● General relativity Metrics, black hole horizon, Hawking radiation

● Bose-Einstein condensates (BECs)● Future directions – quantum gravity

home.tiscali.nl

● Motivation Analogies provide

new ways of looking at a problem

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An analogue model of gravity● Sound waves in a fluid are used as an analogy for

light waves under the effect of gravity

Analogue gravity [1]

http://www.iihr.uiowa.edu/products/dhrm.html

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An analogue model of gravity● Sound waves in a fluid are used as an analogy for

light waves under the effect of gravity “Dumb hole” Video of Supersonic flow

Analogue gravity [1]

http://www.iihr.uiowa.edu/products/dhrm.html

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An analogue model of gravity● Sound waves in a fluid are used as an analogy for

light waves under the effect of gravity “Dumb hole” Video of Supersonic flow

● Unruh predicts Hawking radiation from a dumb hole (Experimental black hole evaporation, W. G. Unruh 1981)

Analogue gravity [1]

http://www.iihr.uiowa.edu/products/dhrm.html

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Advances in analogue gravity● Condensed matter-based models – Superfluids, BECs

Analogue gravity [1]

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Advances in analogue gravity● Condensed matter-based models – Superfluids, BECs ● Wormholes● Slow light● Faster-than-light travel

Analogue gravity [1]

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Advances in analogue gravity● Condensed matter-based models – Superfluids, BECs ● Wormholes● Slow light● Faster-than-light travel● Rotating black holes● Back-reaction● Cosmological particle creation

Analogue gravity [1]

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Advances in analogue gravity● Condensed matter-based models – Superfluids, BECs ● Wormholes● Slow light● Faster-than-light travel● Rotating black holes● Back-reaction● Cosmological particle creation● Quantum gravity

Analogue gravity [1]

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Advances in analogue gravity● Condensed matter-based models – Superfluids, BECs ● Wormholes ● Slow light● Faster-than-light travel● Rotating black holes● Back-reaction● Cosmological particle creation● Quantum gravity

Impact: workshops, conference sessions, books, articles Analogue gravity

[1]

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Model – The Acoustic Metric● First, the black hole and event horizon

www.aip.org

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● First, the black hole and event horizon

● Our model – sound waves propagating in a perfect fluid

www.aip.org

Model – The Acoustic Metric

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Euler's equation for adiabatic, irrotational fluid

This is describes a 'steady flow'

● First, the black hole and event horizon

● Our model – sound waves propagating in a perfect fluid Equation of continuity www.aip.org

Model – The Acoustic Metric

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● Separate fluid components into that of the background fluid motion and sound waves moving in the fluid

Model – The Acoustic Metric

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● Separate fluid components into that of the background fluid motion and sound waves moving in the fluid

● Wave equation for sound waves in the fluid

Model – The Acoustic Metric

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● Separate fluid components into that of the background fluid motion and sound waves moving in the fluid

● Wave equation for sound waves in the fluid

● We can deduce the acoustic metric ‘felt' by sound waves

Model – The Acoustic Metric

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● Separate fluid components into that of the background fluid motion and sound waves moving in the fluid

● Wave equation for sound waves in the fluid

● We can deduce the acoustic metric ‘felt' by sound waves

● and rewrite the wave equation

Model – The Acoustic Metric

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General relativity● Gravity is curved space-time

www.zarm.uni-bremen.dewww.math.skjilawww.colorado.edu/bec/

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General relativity● Gravity is curved space-time● The metric – distance between

objects in curved space-time

www.zarm.uni-bremen.dewww.math.skjilawww.colorado.edu/bec/

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General relativity● Gravity is curved space-time● The metric – distance between

objects in curved space-time

www.zarm.uni-bremen.dewww.math.skjilawww.colorado.edu/bec/

● Einstein's equations

Geometry of space determined by matter

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General relativity● Black holes are described by Schwarzschild metric

www.ifa.hawaii.eduwww.scielo.brwww.dailytech.com

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General relativity● Black holes are described by Schwarzschild metric

www.ifa.hawaii.eduwww.scielo.brwww.dailytech.com

● Hawking radiation thermal radiation from black hole horizon due to

quantum fluctuations (Black hole explosions S. W. Hawking 1974)

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General relativity● Black holes are described by Schwarzschild metric

www.ifa.hawaii.eduwww.scielo.brwww.dailytech.com

● Hawking radiation thermal radiation from black hole horizon due to

quantum fluctuations (Black hole explosions S. W. Hawking 1974)

Also found produced by dumb holes

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The Bose-Einstein Condensate● Predicted in 1920, created in 1995

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The Bose-Einstein Condensate● Predicted in 1920, created in 1995● A Bose-Einstein condensate is a gas of particles in

the lowest quantum energy state ● Quantum effects become visible on a macroscopic

level

www.colorado.edu/physics/2000/bec/

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The Bose-Einstein Condensate● Predicted in 1920, created in 1995● A Bose-Einstein condensate is a gas of particles in

the lowest quantum energy state ● Quantum effects become visible on a macroscopic

level

www.colorado.edu/physics/2000/bec/

Importantly, BEC based models predict measurable sonic radiation from horizon and are relatively easy to conduct experiments with.

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Future directions – quantum gravity

● Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory

www.liftport.com

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Future directions – quantum gravity

● Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory

www.liftport.com

● Analogue models provide good hints to how such a fundamental theory might work

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Future directions – quantum gravity

● Quantum gravity – the idea that general relativity is a low-energy approximation of a more fundamental theory

www.liftport.com

● Analogue models provide good hints to how such a fundamental theory might work

● That's all guys

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References

1. "Analogue Gravity" Carlos Barceló and Stefano Liberati and Matt Visser, Living Rev. Relativity 8, (2005), 12 and references therein

2. “Sonic analogue of gravitational black holes in Bose-Einstein condensates” L. G. Garay, J. R. Anglin, J. I. Cirac, P. Zoller, Phys. Rev. Lett. 85, (2000), 4643

3. “Hydrodynamics” Sir Horace Lamb, “Fluid Mechanics” Landau and Lifshitz, (1959)

4. “Statistical Mechanics” K. Huang, (1987)5. “General relativity primer” Richard H. Price, Am. J. Phys. 50,

(1982), 300, “Gravitation” Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, (1973)

6. “Critical Behaviour in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry” W. G. Unruh, Ignacio Olaberrieta, Jason F. Ventrella, Matthew W. Choptuik – gr-qc/0708.0513

7. “Quantum toy model for black-hole back-reaction” Clovis Maria, Ralf Schützhold – gr-qc/0706.4010

8. “Trans-Planckian physics and signature change events in Bose gas hydrodynamics” Silke Weinfurtner, Angela White, Matt Visser – gr-qc/0703117