TY - JOUR

T1 - Black holes as collapsed polymers

AU - Brustein, Ram

AU - Medved, A. J.M.

N1 - Funding Information:
We would like to thank Itzhak Fouxon, Rony Granek, Sunny Itzhaki, Oleg Krichevsky, Gilad Lifschytz, Costas Skenderis, Marika Taylor and Gabriele Veneziano for valuable discussions. The research of AJMM received support from an NRF Incentive Funding Grant 85353, an NRF Competitive Programme Grant 93595 and Rhodes Research Discretionary Grants. AJMM thanks Ben Gurion University for their hospitality during his visit. The research of RB is supported by the Israel Science Foundation grant no. 1294/16.
Publisher Copyright:
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings at the Hagedorn temperature. According to our proposal, the interior of the BH consists, on average, of a uniform distribution of matter with low curvature and large quantum fluctuations about the average. This proposal represents a dramatic departure from any conventional state of matter and from the longstanding expectation that the interior of a BH should look like empty space except for a very small, dense core (the singularity). Standard effective field theory in terms of the metric and other quantum fields is incapable of describing such a state in a meaningful way. However, in polymer physics, such states can be described by a mean field theory in terms of the polymer concentration. We therefore propose that the interior of the BH be described in terms of an effective free-energy density which is a function of the string concentration or entropy density; this density being a highly non-perturbative quantity in terms of the metric and other quantum fields. For a macroscopic BH, our proposed free-energy density contains only linear and quadratic terms, in analogy with that of the theory of collapsed polymers. We calculate the coefficient of the linear term under the accepted assumption that the dominant interaction of the strings at large distances is the gravitational interaction and the coefficient of the quadratic term by relying on explicit string calculations to determine the rate of interaction in terms of the string coupling. Using the effective free energy, we find that the size of the bound state is determined dynamically by the string attractive interactions and derive scaling relations for the entropy, energy and size of the bound state. We show that these agree with the scaling relations of the BH; in particular, with the area law for the BH entropy. The fact that the entropy is not extensive is a result of having strong correlations in the interior state, and the specific form of the entropy-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.

AB - We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings at the Hagedorn temperature. According to our proposal, the interior of the BH consists, on average, of a uniform distribution of matter with low curvature and large quantum fluctuations about the average. This proposal represents a dramatic departure from any conventional state of matter and from the longstanding expectation that the interior of a BH should look like empty space except for a very small, dense core (the singularity). Standard effective field theory in terms of the metric and other quantum fields is incapable of describing such a state in a meaningful way. However, in polymer physics, such states can be described by a mean field theory in terms of the polymer concentration. We therefore propose that the interior of the BH be described in terms of an effective free-energy density which is a function of the string concentration or entropy density; this density being a highly non-perturbative quantity in terms of the metric and other quantum fields. For a macroscopic BH, our proposed free-energy density contains only linear and quadratic terms, in analogy with that of the theory of collapsed polymers. We calculate the coefficient of the linear term under the accepted assumption that the dominant interaction of the strings at large distances is the gravitational interaction and the coefficient of the quadratic term by relying on explicit string calculations to determine the rate of interaction in terms of the string coupling. Using the effective free energy, we find that the size of the bound state is determined dynamically by the string attractive interactions and derive scaling relations for the entropy, energy and size of the bound state. We show that these agree with the scaling relations of the BH; in particular, with the area law for the BH entropy. The fact that the entropy is not extensive is a result of having strong correlations in the interior state, and the specific form of the entropy-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.

KW - Black hole thermodynamics

KW - Quantum Black holes

UR - http://www.scopus.com/inward/record.url?scp=85008939489&partnerID=8YFLogxK

U2 - 10.1002/prop.201600114

DO - 10.1002/prop.201600114

M3 - Article

AN - SCOPUS:85008939489

VL - 65

JO - Fortschritte der Physik

JF - Fortschritte der Physik

SN - 0015-8208

IS - 1

M1 - 1600114

ER -