  We investigate 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 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.
