Chaos in Matrix Models and Black Hole Evaporation

TL;DR

This paper investigates black hole evaporation using matrix quantum mechanics, revealing chaotic dynamics, negative specific heat, and possible holographic interpretations, thereby providing insights into unitarity and Hawking radiation.

Contribution

It introduces a matrix model approach to black hole evaporation, highlighting chaos, negative specific heat, and a geometric interpretation of matrix eigenvalues in holography.

Findings

Black zero-branes exhibit negative specific heat similar to Schwarzschild black holes.

Chaos increases during evaporation, with Lyapunov exponent growing.

Kolmogorov-Sinai entropy decreases as the black hole evaporates.

Abstract

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.