Black Holes in Matrix Theory

Matrix theory [1] appears to capture a remarkable amount of the nonperturbative structure of string/M-theory. At generic values of the moduli, most of the localized states of the latter are black holes. One would like to see how matrix theory encodes their basic properties { geometry, dynamics of test particles, thermodynamics, decay via the Hawking process, etc. First steps in this direction have recently been taken [2]-[3]; our purpose here is to summarize the results (with a few extensions), as well as to argue for a general picture of black hole structure. We begin in section 2 with a discussion of the geometry we are trying to reproduce { classical eleven-dimensional supergravity. The focus is on ve-dimensional (near)BPS black holes [5] (for a review, see [6]), as these are best understood from the standpoint of string theory. We then point out a few properties of supergravitons as probes of the geometry, and indicate how matrix theory reproduces various asymptotic features of the metric. Adapting a D-brane calculation of Maldacena [7], we reproduce in section 3 the near-extremal black hole entropy as the entropy of the noncritical string theory that describes matrix theory on T 5 [4,8]. Rephrasing the calculation in natural M-theory variables renders the interpretation of many formulae transparent. The basic theme will be that black hole thermodynamics is generalized supersymmetric Yang-Mills statistical mechanics, in the microcanonical ensemble.