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Title: Chaos in matrix models and black hole evaporation

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest thatmore » by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Stanford Univ., Stanford, CA (United States); Kyoto Univ., Kyoto (Japan)
  3. Univ. of California, Berkeley, CA (United States); Stanford Univ., Stanford, CA (United States)
Publication Date:
Report Number(s):
LLNL-JRNL-681857
Journal ID: ISSN 2470-0010; PRVDAQ; TRN: US1800946
Grant/Contract Number:
AC52-07NA27344
Type:
Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 94; Journal Issue: 12; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS
OSTI Identifier:
1416510
Alternate Identifier(s):
OSTI ID: 1336877

Berkowitz, Evan, Hanada, Masanori, and Maltz, Jonathan. Chaos in matrix models and black hole evaporation. United States: N. p., Web. doi:10.1103/PhysRevD.94.126009.
Berkowitz, Evan, Hanada, Masanori, & Maltz, Jonathan. Chaos in matrix models and black hole evaporation. United States. doi:10.1103/PhysRevD.94.126009.
Berkowitz, Evan, Hanada, Masanori, and Maltz, Jonathan. 2016. "Chaos in matrix models and black hole evaporation". United States. doi:10.1103/PhysRevD.94.126009. https://www.osti.gov/servlets/purl/1416510.
@article{osti_1416510,
title = {Chaos in matrix models and black hole evaporation},
author = {Berkowitz, Evan and Hanada, Masanori and Maltz, Jonathan},
abstractNote = {Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.},
doi = {10.1103/PhysRevD.94.126009},
journal = {Physical Review D},
number = 12,
volume = 94,
place = {United States},
year = {2016},
month = {12}
}