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 realtime dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zerobrane) 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 D0branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zerobrane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0branes. While the largest Lyapunov exponent grows during the evaporation, the KolmogorovSinai 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 Mtheory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest thatmore »
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Stanford Univ., Stanford, CA (United States); Kyoto Univ., Kyoto (Japan)
 Univ. of California, Berkeley, CA (United States); Stanford Univ., Stanford, CA (United States)
 Publication Date:
 Report Number(s):
 LLNLJRNL681857
Journal ID: ISSN 24700010; PRVDAQ; TRN: US1800946
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 94; Journal Issue: 12; Journal ID: ISSN 24700010
 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 realtime dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zerobrane) 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 D0branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zerobrane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0branes. While the largest Lyapunov exponent grows during the evaporation, the KolmogorovSinai 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 Mtheory 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}
}