Chaos in matrix models and black hole evaporation

Journal Article · Mon Dec 19 00:00:00 EST 2016 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.94.126009· OSTI ID:1416510

Berkowitz, Evan ^[1]; Hanada, Masanori ^[2]; Maltz, Jonathan ^[3]

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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)

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1416510
• Alternate ID(s): OSTI ID: 1336877
• Report Number(s): LLNL-JRNL--681857
• Journal Information: Physical Review D, Journal Name: Physical Review D Journal Issue: 12 Vol. 94; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTRONOMY AND ASTROPHYSICS