Past horizons in D-dimensional Robinson-Trautman spacetimes

TL;DR

This paper generalizes the Penrose--Tod equation to higher-dimensional Robinson--Trautman spacetimes with cosmological constant and radiation, proving the existence of past horizons in dimensions greater than four using nonlinear PDE techniques.

Contribution

It introduces a higher-dimensional version of the Penrose--Tod equation and proves the existence of past horizons in D>4 dimensions, extending previous four-dimensional results.

Findings

Existence of solutions for the generalized equation in D>4 dimensions.

The past horizon is a trapping and dynamical horizon.

Generalization of four-dimensional results to higher dimensions.

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. Existence of its solutions in $D>4$ dimensions is proved using tools for nonlinear elliptic partial differential equations. We show that this horizon is naturally a trapping and a dynamical horizon. The findings generalize results from D=4.