Entanglement Entropy for the Black 0-Brane

TL;DR

This paper investigates the entanglement entropy of Hawking radiation from the Black 0-Brane, demonstrating the Page curve and information recovery through a quantum mechanical model linked to supergravity and matrix theory.

Contribution

It introduces a novel Hilbert space framework for describing partially evaporated black holes and computes the entanglement entropy consistent with the Page curve in this context.

Findings

Reproduction of the Page curve for the Black 0-Brane system.

Entanglement entropy depends on geometric parameters of the black hole.

A new Hilbert space formalism for partial black hole evaporation.

Abstract

We analyse the entanglement entropy between the Black 0-Brane solution to supergravity and its Hawking radiation. The Black 0-Brane admits a dual Gauge theory description in terms of the Matrix model for M-Theory, named BFSS theory, which is the theory of open strings on a collection of N D0-branes. Recent studies of the model have highlighted a mechanism of Black Hole evaporation for this system, based on the chaotic nature of the theory and the existence of flat directions. This paper further explores this idea, through the computation of the von Neumann entropy of Hawking radiation. In particular, we show that the expected Page curve is indeed reproduced, consistently with a complete recovery of information after the Black Hole has fully evaporated. A pivotal step in the computation is the definition of a Hilbert space which allows for a quantum mechanical description of partially evaporated Black Holes. We find that the entanglement entropy depends on the choice of a parameter, which can be interpreted as summarizing the geometric features of the Black Hole, such as the size of the resolved singularity and the size of the horizon.