Classical black hole production in high-energy collisions

We investigate the classical formation of a D-dimensional black hole in a high-energy collision of two particles. The existence of an apparent horizon is related to the solution of an unusual boundary-value problem for Poisson's equation in flat space. For a sufficiently small impact parameter, we construct solutions giving such apparent horizons in $D=4.$ These supply improved estimates of the classical cross section for black hole production, and of the mass of the resulting black holes. We also argue that a horizon can be found in a region of weak curvature, suggesting that these solutions are valid starting points for a semiclassical analysis of quantum black hole formation.