Quantum state of the black hole interior

Fortschritte der Physik

2016

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We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings at the Hagedorn temperature. The size of the bound state is smaller than the string random-walk scale and determined dynamically by the string attractive interactions. It is further proposed that the effective free-energy density of the bound state should be expressed as a function of its entropy density. For a macroscopic BH, the free-energy density contains only linear and quadratic terms, in analogy with that of a collapsed polymer when expressed as a function of the polymer concentration. Using the effective free energy, we derive scaling relations for the entropy, energy and size of the bound state and show that these agree with the scaling relations of the BH; in particular, with the area law for the BH entropy. The area law originates from the inverse scaling of the effective temperature with the bound-state radius. We also find that the energy density of the bound state is equal to its pressure.Comment: 20 page

“…As mentioned in , the relation

p = ρ

coincides with the saturation of the causal entropy bound , indicating the breakdown of semiclassical physics , which is consistent with the notion of a highly quantum state. The equation of state

p = ρ

Section: Introductionsupporting

confidence: 82%

“…We also argued in for the “no‐remnant” condition: The entropy that is enclosed by a spherical shell at any radius

r < R_{S}

cannot exceed that of the Bekenstein–Hawking area‐law . This condition implies large deviations from the general‐relativistic picture of mostly empty space with a highly dense core.…”

Section: Introductionmentioning

confidence: 82%

Black holes as collapsed polymers

Fortschritte der Physik

2016

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“…Similar claims about the non-classicality of Hawking radiation, in spite of its apparent thermal nature, have been put forth in an earlier article [1], and the possible consequences of this non-classicality were subsequently discussed in [2][3][4]. In these studies, however, no detailed evidence was provided except to point out that the occupation numbers of the Hawking modes are inevitably small.…”

Section: Introductionmentioning

confidence: 60%

The state of Hawking radiation is non-classical

Zigdon

2018

J. High Energ. Phys.

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We show that the state of the Hawking radiation emitted from a large Schwarzschild black hole (BH) deviates significantly from a classical state, in spite of its apparent thermal nature. For this state, the occupation numbers of single modes of massless asymptotic fields, such as photons, gravitons and possibly neutrinos, are small and, as a result, their relative fluctuations are large. The occupation numbers of massive fields are much smaller and suppressed beyond even the expected Boltzmann suppression. It follows that this type of thermal state cannot be viewed as classical or even semiclassical. We substantiate this claim by showing that, in a state with low occupation numbers, physical observables have large quantum fluctuations and, as such, cannot be faithfully described by a mean-field or by a WKB-like semiclassical state. Since the evolution of the BH is unitary, our results imply that the state of the BH interior must also be non-classical when described in terms of the asymptotic fields. We show that such a non-classical interior cannot be described in terms of a semiclassical geometry, even though the average curvature is sub-Planckian.

“…The BH has the same equation of state,

s = \sqrt{ρ}

, if the interior matter is distributed so as to saturate the Bekenstein–Hawking entropy–area law for any interior, closed surface . The same equation of state also signals the saturation of the causal entropy bound which implies, in turn, the breakdown of semiclassical physics .…”

Section: Introductionmentioning

confidence: 99%

Emergent horizon, Hawking radiation and chaos in the collapsed polymer model of a black hole

2017

Fortschr. Phys.

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We have proposed that the interior of a macroscopic Schwarzschild black hole (BH) consists of highly excited, long, closed, interacting strings and, as such, can be modeled as a collapsed polymer. It was previously shown that the scaling relations of the collapsed-polymer model agree with those of the BH. The current paper further substantiates this proposal with an investigation into some of its dynamical consequences. In particular, we show that the model predicts, without relying on gravitational effects, an emergent horizon. We further show that the horizon fluctuates quantum mechanically as it should and that the strength of the fluctuations is inversely proportional to the BH entropy. It is then demonstrated that the emission of Hawking radiation is realized microscopically by the quantum-induced escape of small pieces of string, with the rate of escape and the energy per emitted piece both parametrically matching the Hawking temperature. We also show, using standard methods from statistical mechanics and chaos theory, how our model accounts for some other known properties of BHs. These include the accepted results for the scrambling time and the viscosity-to-entropy ratio, which in our model apply not only at the horizon but throughout the BH interior.