On boosted space-times with cosmological constant and their ultrarelativistic limit

TL;DR

This paper derives a shock-wave geometry with a cosmological constant by boosting an exact Schwarzschild-de Sitter (or anti-de Sitter) black hole, revealing a distributional singularity on a null hypersurface through a non-perturbative approach.

Contribution

It provides an exact, non-perturbative derivation of shock-wave geometries with cosmological constant, confirming previous linearized results with a novel exact calculation.

Findings

Distributional singularity on a null hypersurface identified

Exact non-perturbative derivation matches previous linearized results

Peculiar cancellations occur in the exact metric calculation

Abstract

The problem of deriving a shock-wave geometry with cosmological constant by boosting a Schwarzschild-de Sitter (or anti-de Sitter) black hole is re-examined. Unlike previous work in the literature, we deal with the exact Schwarzschild-de Sitter (or anti-de Sitter) metric. By virtue of peculiar cancellations in this exact calculation, where the metric does not depend linearly on the mass parameter, we find a singularity of distributional nature on a null hypersurface, which corresponds to a shock-wave geometry derived in a fully non-perturbative way. The result agrees with previous calculations, where the metric had been linearized in the mass parameter.