Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita--Bertotti--Robinson

TL;DR

This paper analyzes the ultrarelativistic limit of a black hole in a magnetic universe, resulting in an impulsive gravitational wave with specific geometric features, connecting to known wave solutions.

Contribution

It provides an exact solution describing a boosted black hole in a magnetic universe and clarifies its relation to known gravitational wave families.

Findings

The ultrarelativistic limit yields a non-expanding impulsive wave in the LCBR universe.

The wave front is a 2-sphere with two null particles at its poles.

The solution belongs to the Kundt class of spacetimes.

Abstract

We consider an exact Einstein-Maxwell solution constructed by Alekseev and Garcia which describes a Schwarzschild black hole immersed in the magnetic universe of Levi-Civita, Bertotti and Robinson (LCBR). After reviewing the basic properties of this spacetime, we study the ultrarelativistic limit in which the black hole is boosted to the speed of light, while sending its mass to zero. This results in a non-expanding impulsive wave traveling in the LCBR universe. The wave front is a 2-sphere carrying two null point particles at its poles -- a remnant of the structure of the original static spacetime. It is also shown that the obtained line-element belongs to the Kundt class of spacetimes, and the relation with a known family of exact gravitational waves of finite duration propagating in the LCBR background is clarified. In the limit of a vanishing electromagnetic field, one point particle is pushed away to infinity and the single-particle Aichelburg-Sexl pp-wave propagating in Minkowski space is recovered.