Existence of horizons in Robinson-Trautman spacetimes of arbitrary dimension

Abstract

We derive the higher dimensional generalization of Penrose-Tod equation describing past horizon in Robinson-Trautman spacetimes with a cosmological constant and pure radiation. Results for D=4 dimensions are summarized. Existence of its solutions in D>4 dimensions is proved using tools for nonlinear elliptic partial differential equations.Comment: to appear in proceedings of MGM12 Paris, Franc