Thermal Duality: Nemesis of Black

Holes?Mike Hewitt

Canterbury Christ Church University

What is the thermalon?

• Condensate that forms at the Hagedorn transition.

• Euclidean single wrapping mode – related to the thermal path integral for a single string by modular invariance.

• The thermalon mode will be interpreted as a deformation of the vacuum, in thermal equilibrium with normal vacuum.

• The thermalon is not a normal propagating state – rather, a macroscopic order parameter for mixing long string states with the field vacuum, entangling the external field state with long strings.

Thermalon and gravity

• Why is the thermalon relevant to gravity?

• Heterotic strings: for Left moving currents and their interaction vertex, at the dual point:

(thermalon, graviton) is equivalent to (W,).

Gravito-thermal interaction

• The thermalon is part of the gravity sector in string theory.

• Gravity becomes part of a ‘gravito-thermal’ interaction.

• The condensate that forms at the Hagedorn transition behaves as part of the gravity sector.

• Thermal duality implies a possibility of the thermalon producing gravitational vacuum polarization.

• This may limit the strength of gravity, preventing the formation of black holes – a novel macroscopic effect.

Why is this significant?

• String theory does not work in 4 dimensions without a gravity regulator – more below.

• With a regulator, it may become like QCD, with gravitationally free strings confined to a bag of a different phase.

• The heterotic gravity regulator is generic in dimension, and avoids black hole formation and related information paradoxes.

• The heterotic regulator may generalise to other string models.

Scaling behaviour vs dimension

Holographic principle

Problem of strings in 4 dimensions

• An attractive feature of string theory is that it naturally includes gravitons and has finite amplitudes for graviton scattering in the critical dimension.

• High energy scattering is intermediated by an infinite spectrum of free string states.

• However, string theory as a theory of quantum gravity does not really work as advertised in 4 dimensions, as high energy collisions would form black holes rather than demonstrate string scattering amplitudes or the production of long string states.

Free string spectrum

…operators

Average

String radial scale

• It appears that most string states would collapse behind event horizons.

• However, the fixed nature of the value for the transition temperature from the winding mode implies that the free spectrum is somehow preserved when gravity is turned on.

• This supports a bag model interpretation for string states in 4 dimensions (hadron analogy).

Thermal duality – to the rescue?

• Maximum of Z against from thermal duality indicates that the greatest density of strings and information is around the self-dual temperature.

• Heterotic string case is discussed here primarily for simplicity as they are pure string models [Polchinski hep-th/050033] with explicit thermal duality.

Thermalon weak field solutions

Accelerating Wall Solution

• Note the negative energy density close to the horizon

• Source is zero at

Red Shifted Source (Seen from infinity)

Area Difference across the Wall

• This can be described by a ‘warp factor’ w:

Gravity Regulator proposal• Galileo – Einstein: The acceleration of convex surfaces with

locally constant area is limited by the Hagedorn Rindler acceleration.

• Newton: heuristic equivalent – the gravitational force between any 2 objects (from or local static c.m. frames) is limited by the string tension.

• This Newtonian form shows the mutual interactive nature of the effect, as a phenomenon of the gravito-thermal interaction.

• Both forms apply in all dimensions for heterotic strings.

• Not related to the magnitude of the tidal Riemannian curvature!

Adiabatic (constant area) condition

Critical acceleration

Convexity

Generalisation

• Note the generic nature of the conditions, which can be abstracted from the heterotic context, and may apply across M space.

• The differential geometry applies in all uncompactified dimensions.

• The mechanism for heterotic strings relies on the self-dual nature of the thermalon. Although the thermalon is not self-dual for non-heterotic strings, thermal duality may still apply to the string sector (T duality in Euclidean time).

Non-heterotic case

• Mertens, Verschelde & Zakharov obtained similar results for the Rindler solution stress tensor for thermalons in type II string models. [arXiv:1408.7012]

• Although these models do not have explicit thermal duality, this behaviour is related to the T duality of the torus diagram.

The conjecture also implies that (some generalisation of) thermal duality also provides a gravitational regulator for 11 dimensional supergravity.

Gravity regulator properties• Critical surface conditions are a string regularised version

of a Penrose trapped surface (infinite tension limit).

• Horizons are defined globally but trapped surfaces (and thermalon traps) are defined locally by these geometric conditions.

• Heuristically the critical gravity condition for conversion is equivalent to the condition that the Newtonian gravity (in local centre of mass frame) between any two objects is limited by the string tension.

• Mutual nature of effect between two interacting bodies is shown by the symmetry of the ‘Newtonian’ effective criterion for the gravitational regulator – may also hold throughout M space.

Transition• A thermalon shell region is stable on the outside, unstable/dynamic on

the inside.

• Assume that thermalon polarization maintains gravitational regulation

• Transition begins at a separation between virtual horizons.

• Deceleration may couple matter to thermalon production to give a stringy bremsstrahlung process, converting kinetic energy to thermalons – a dynamic aspect of the gravito-thermal interaction.

• Conversion power is constant ~ T (string tension) throughout relative to local static frames. This is consistent with a gravity sector effect.

• Progressively thickening solutions would be produced during conversion after transition to the non-linear regime – limit is the ball solution.

Transition Process

• The following slide shows a possible transition processes for formation of a thermalon region and absorption of infalling matter.

• The infalling matter has a relativistic velocity relative to the interior.

Encounter process

• Diagrams:

Conversion timescales

• Relativistic factors for time dilation:

• for formation• for particle absorption

(d is distance from the existing boundary)

• This gives new estimates for transition times (from infinity):

for initial formation, for particle absorption.

Conversion from Minkowski space?

• Suppose a planar thermalon trap crosses a wall of matter in Minkowski space.

• The wall of matter cannot be converted to a thermalon excitation because of the warp factor that would be produced.

• Agrees with intuition about conservation of energy.

• Conversion is not possible in Minkowski space.

Particle absorption

• Consider next a thermalon front geometry with a salient (previous diagram). Could this be produced by a thermalon trap absorbing a particle in Minkowski space?

• An expanding wave-front bounds a convex region in a Minkowski background. This is inconsistent with a locally constant area.

• Thus, although traps associated with Rindler frames are everywhere in Minkowski space, these cannot gain energy by recruiting particles.

Ball solution

• Thermal duality implies that gravitational gradients are expelled around the self-dual point. This is similar to the Meissner effect in superconductors.

[MH arxiv 1309.7578]

• Gravitational polarization gives a screening mechanism which restricts the gravitational source to the boundary of a (fully developed) thermalon region.

• Hyperbolic spatial geometry in the interior makes the volume and information content proportional to surface area.

• String excitations are gravitationally free in the interior – like quarks in hadrons.

• Should resolve string state problem in 4 dimensions.

Hot objects

• The ball solution is in thermal equilibrium with the exterior normal vacuum.

• A hot object with matching temperature and surface gravity can be in thermal equilibrium with normal vacuum, with

= 0 in the exterior space.

• In general, the surface temperature and gravity would only match (i.e ) by coincidence and the object would be unstable.

Naturalness of the thermalon ball

• A thermalon deformation however naturally and stably meets this matching condition for temperature and surface gravity as it is tied to the location of high static gravitational acceleration.

• Here a ‘standing wave’ thermalon excitation can ride the gravitational field.

Black holes and M theory• To resolve short distances requires concentrating high

energy into a small volume - at increasing energy, eventually gravity becomes strong over longer distances, and the resolution deteriorates again.

• Making gravity consistent with quantum mechanics is problematic for this reason, and problems with macroscopic collapsed objects (e.g. evaporation paradoxes) will also be present for

• We therefore expect that a gravitational regulator mechanism should generalise to all regions of M theory and all compactifications, as all will have collapsed states, and so need to avoid paradoxes associated with black holes.

Evaporating Black Hole

• Note the causal disconnection between the original information and late Hawking radiation.

• Monogamy of entanglement prevents reconciliation of ‘lost’ and ‘found’ information.

Black hole evaporation paradoxes

• General problem – getting information out from a photon trap – without propagating information faster than light (outside the light cone).

• A resort to quantum mechanics for a resolution does not seem to work –inconsistent with the principles of quantum information theory

• Braunstein - Pirandola theorems – the conventional picture of black hole evaporation appears to be inconsistent with unitarity [arXiv:1411.7195] .

Unitarity problems [B-P]

Theorem 1: A contradiction exists between:

• 1.a) completely unitarily evaporating black holes, • 1.b) a freely falling observer notices nothing

special until they pass well within a large black hole's horizon, and

• 1.c) the black hole interior Hilbert space dimensionality may be well approximated as the exponential of the Bekenstein Hawking entropy.

Theorem 2: A contradiction exists between:

• 2.a) completely unitarily evaporating black holes,

• 2.b) large black holes are described by local physics (no signals faster than light)

and

• 2.c) externally, a large black hole should resemble its classical theoretical counterpart (aside from its slow evaporation).

Holographic problem

• Issue with holographic principle for stellar collapse:

• Information content of star ~ bits exceeds the holographic limit before reaching the singularity.

• String physics apparently not relevant at this point, in the usual interpretation.

Resolution?

• This model may resolve ‘firewall paradoxes’ by removing the horizon, and providing a physically motivated firewall to store the information content of a collapsing object.

• The ‘firewall’ here would be formed by string bremsstrahlung during gravitational collapse.

• The firewall would be stable - there is no black hole, and the interior space has been crushed so there is nowhere else for the energy and information to go except outward by Hawking evaporation.

Conclusions• Because of thermal duality, string models may

have a vacuum polarization mechanism which limits the strength of gravity.

• The criterion for this to be effective is based on the area of accelerating surfaces, not the tidal Riemannian curvature.

• This effect would occur at, and only at, sites of extreme

gravitational collapse.• Collapsing objects would form hot holograms,

rather than black holes.• This would resolve the firewall paradox: firewalls

are real, but black holes are not.• Resolve the black hole information problem: there

would be no black holes to compromise quantum information.