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.

Keywords

• general relativity
• Robinson-Trautman spacetime
• higher dimensions