Chaos in matrix models and black hole evaporation
Volume
94
Pagination
126009 - ?
Publisher
DOI
10.1103/physrevd.94.126009
Journal
Physical Review D
Issue
ISSN
2470-0010
Metadata
Show full item recordAbstract
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. Finally, 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.
Authors
Berkowitz, E; Hanada, M; Maltz, JCollections
- Mathematics [1686]