Chaos in Matrix Models and Black Hole Evaporation

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.

18 Pages, 4 Figures,a few minor miscalculations in Sec.4.3 have been corrected, the conclusion remains unchanged

References in corpus (8)

• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Black hole thermodynamics from simulations of lattice Yang-Mills theory
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• Chaos in Classical D0-Brane Mechanics
• High temperature expansion in supersymmetric matrix quantum mechanics
• Gauge/gravity duality and lattice simulations of one dimensional SYM with sixteen supercharges
• Quantum Black Hole Formation in the BFSS Matrix Model
• Monte Carlo approach to the string/M-theory

Cited by in corpus (23)

• Bounding the Space of Holographic CFTs with Chaos
• A proposal of the gauge theory description of the small Schwarzschild black hole in AdS${}_5\times$S${}^5$
• Out-of-time-order correlator in coupled harmonic oscillators
• Anatomy of Deconfinement
• Partial Deconfinement
• Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
• Partial-Symmetry-Breaking Phase Transitions
• Permutation Orbifolds and Chaos
• Angular momentum and chaos bound of charged particles around Einstein-Euler-Heisenberg AdS black holes
• Bulk geometry in gauge/gravity duality and color degrees of freedom
• Precision test of gauge/gravity duality in D0-brane matrix model at low temperature
• Soft-Hair-Enhanced Entanglement Beyond Page Curves in a Black-hole Evaporation Qubit Model
• Matrix Entanglement
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Classical and quantum butterfly effect in nonlinear vector mechanics
• Four-point function in the IOP matrix model
• Black Hole and Fuzzy Objects in BFSS Matrix Model
• Scrambling under quench
• Improved semiclassical model for real time evaporation of Matrix black holes
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Chaos in the holographic matrix models for meson and baryon
• Entanglement Entropy for the Black 0-Brane
• Fuzzy Black Holes from Mass Generation in Matrix Compactification