Black holes and black strings in plane waves

TL;DR

This paper explores the construction of black holes and black strings in vacuum plane wave spacetimes, revealing the existence of regular black string solutions but not black holes, and highlighting restrictions on asymptotic solutions.

Contribution

It introduces a method to find solutions in plane wave backgrounds and demonstrates the existence of regular black strings but not black holes within this framework.

Findings

Regular black string solutions are found.

No regular black hole solutions are found.

Asymptotic solutions are restricted by new conditions.

Abstract

We investigate the construction of black holes and black strings in vacuum plane wave spacetimes using the method of matched asymptotic expansions. We find solutions of the linearised equations of motion in the asymptotic region for a general source on a plane wave background. We observe that these solutions do not satisfy our previously defined conditions for being asymptotically plane wave. Hence, the space of asymptotically plane wave solutions is restricted. We consider the solution in the near region, treating the plane wave as a perturbation of a black object, and find that there is a regular black string solution but no regular black hole solution.