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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 boundaryvalue 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.

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