SCHWARZSCHILD BLACK-HOLES FROM MATRIX-THEORY

We consider matrix theory compactified on T-3 and show that it correct ly describes the properties of Schwarzschild black holes in 7 + 1 dime nsions, including the mass-entropy relation, the Hawking temperature, and the physical size, up to numerical factors of order unity. The mos t economical description involves setting the cutoff N in the discreti zed light-cone quantization to be of order the black hole entropy. A c rucial ingredient necessary for our work is the recently proposed equa tion of state for 3 + 1 dimensional supersymmetric Yang-Mills theory w ith 16 supercharges. We give detailed arguments for the range of valid ity of this equation following the methods of Horowitz and Polchinski.