On Schwarzschild Black Hole in Large N Matrix theory

TL;DR

This paper explores the description of Schwarzschild black holes within large N Matrix theory, proposing an entropy formula consistent with black hole thermodynamics and demonstrating Newtonian gravity between black holes, supporting Lorentz invariance.

Contribution

It introduces a new entropy formula for Schwarzschild black holes in Matrix theory applicable across multiple dimensions and proves Newtonian gravity between unequal mass black holes.

Findings

Entropy formula reproduces SBH thermodynamics in large N limit.

Equations of state derived for low temperature regime.

Proof of Newton's law between two SBHs with different masses.

Abstract

D0-brane gas picture of Schwarzschild black hole (SBH) is considered in the large N regime of Matrix theory. An entropy formula, which reproduces the thermodynamics of SBH in the large N limit for all dimensions ($D\geq 6$), is proposed. The equations of states for low temperature are obtained. We also give a proof of the Newton gravitation law between two SBHs, whose masses are not equal. Our result in some extent supports that the physics of Matrix theory is Lorentz invariant.