Global structure of Robinson-Trautman radiative space-times with cosmological constant

TL;DR

This paper analyzes Robinson-Trautman radiative space-times with a cosmological constant, showing their asymptotic approach to Schwarzschild-de Sitter or anti-de Sitter solutions and examining their global structure and horizon smoothness.

Contribution

It provides a detailed analysis of the global structure and horizon smoothness of Robinson-Trautman space-times with non-zero cosmological constant, including the first example of a smooth but non-analytic horizon.

Findings

Space-times approach Schwarzschild-(anti-)de Sitter solutions at large retarded times.

Horizon smoothness increases for positive Lambda and decreases for negative Lambda.

Identifies a unique case with smooth but non-analytic horizon at 9Lambda m^2=1.

Abstract

Robinson-Trautman radiative space-times of Petrov type II with a non-vanishing cosmological constant Lambda and mass parameter m>0 are studied using analytical methods. They are shown to approach the corresponding spherically symmetric Schwarzschild-de Sitter or Schwarzschild-anti-de Sitter solution at large retarded times. Their global structure is analyzed, and it is demonstrated that the smoothness of the extension of the metrics across the horizon, as compared with the case Lambda=0, is increased for Lambda>0 and decreased for Lambda<0. For the extreme value 9Lambda m^2=1, the extension is smooth but not analytic. This case appears to be the first example of a smooth but not analytic horizon. The models with Lambda>0 exhibit explicitly the cosmic no-hair conjecture under the presence of gravitational waves.