Comments on Black Holes in Matrix Theory

TL;DR

This paper critically examines the application of matrix theory to black hole entropy, highlighting the limitations of current approaches and proposing that the true black hole dynamics are better described by super Yang-Mills theory.

Contribution

It clarifies the regime where matrix theory describes black strings versus black holes and suggests the zero modes of super Yang-Mills theory as the correct description for black hole entropy.

Findings

Matrix theory describes black strings near the transition to black holes.

Black hole entropy may be explained by zero modes of super Yang-Mills theory.

Implications for matrix theory and holography are discussed.

Abstract

The recent suggestion that the entropy of Schwarzschild black holes can be computed in matrix theory using near-extremal D-brane thermodynamics is examined. It is found that the regime in which this approach is valid actually describes black strings stretched across the longitudinal direction, near the transition where black strings become unstable to the formation of black holes. It is argued that the appropriate dynamics on the other (black hole) side of the transition is that of the zero modes of the corresponding super Yang-Mills theory. A suggestive mean field theory argument is given for the entropy of black holes in all dimensions. Consequences of the analysis for matrix theory and the holographic principle are discussed.