Chaos in Matrix Models and Black Hole Evaporation

TL;DR

The paper uses the BFSS matrix model to study black hole formation and real-time evaporation under gauge/gravity duality. It shows that chaos plus flat directions drive D0-brane emission, producing a Hawking-like evaporation with negative specific heat and a decreasing KS entropy despite rising Lyapunov exponents. The authors extend the discussion to the M-theory regime where massless Hawking radiation may be captured by eigenvalue dynamics, and propose a phenomenological real-time model to simulate the full life cycle of a black hole from formation to evaporation. These results connect matrix-model dynamics to gravitational phenomena via eigenvalue distributions and offer a path toward incorporating quantum corrections in a unitary, holographic framework.

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.

Figures (4)

• Figure 1: A possible geometric interpretation of the eigenvalue distribution.
• Figure 2: A phenomenological model of the black zero-brane / Black Hole.
• Figure 3: The observed numerical value of $c_{N,d}/(2N-3)$ as a function of $N$, for several values of $N$ and $d$. Thin black lines indicate where $c_{N,d}=(d-1)(2N-3)$ as in \ref{['eq:dimensional_analysis']}. We fit a line to every span of points to the right of the maximum of the corresponding numerical distribution and constructed a weighted histogram according to goodness of fit. The best values correspond to the maximum of that histogram, while the error bars were determined by finding where that histogram fell by a factor of $e$ to either side.
• Figure 4: The observed numerical distribution as a function of $r$ for $N=2$, $d=3,4,6,9$. The powers $c_{2,d}$ take the same values within error. We divide by $d$ simply to visually offset the different distributions from one another.