Matrix Theory Description of Schwarzschild Black Holes in the Regime N >> S

TL;DR

This paper develops a matrix theory framework to describe Schwarzschild black holes with large entropy, revealing potential higher-dimensional analogues and a new matrix theory generalization involving N^3 degrees of freedom.

Contribution

It derives a general matrix theory equation of state for Schwarzschild black holes and explores their higher-dimensional and brane generalizations.

Findings

Matrix theory equation of state matches various black hole cases.

Higher-dimensional black holes can be described via auxiliary matrix theories.

A special case involves N^3 dynamical degrees of freedom.

Abstract

We study the description of Schwarzschild black holes, of entropy S, within matrix theory in the regime $N \ge S \gg 1$. We obtain the most general matrix theory equation of state by requiring that black holes admit a description within this theory. It has a recognisable form in various cases. In some cases a D dimensional black hole can plausibly be thought of as a $\tilde{D} = D + 1$ dimensional black hole, described by another auxiliary matrix theory, but in its $\tilde{N} \sim S$ regime. We find what appears to be a matrix theory generalisation to higher dynamical branes of the normalisation of dynamical string tension, seen in other contexts. We discuss a further possible generalisation of the matrix theory equation of state. In a special case, it is governed by $N^3$ dynamical degrees of freedom.