Matrix theory description of Schwarzschild black holes in the regime N≫S

We study the description of Schwarzschild black holes, of entropy S, within matrix theory in the regime N≳S≫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 recognizable form in various cases. In some cases a D dimensional black hole can plausibly be thought of as a D̃=D+1 dimensional black hole, described by another auxiliary matrix theory, but in its Ñ∼S regime. We find what appears to be a matrix theory generalization to higher dynamical branes of the normalization of dynamical string tension, seen in other contexts. We discuss a further possible generalization of the matrix theory equation of state. In a special case, it is governed by N³ dynamical degrees of freedom.