Null particle solutions in three-dimensional (anti-) de Sitter spaces

TL;DR

This paper derives exact solutions for null particles in three-dimensional (anti-) de Sitter spaces, including boosted black holes and multiple null particles, highlighting differences from four-dimensional cases.

Contribution

It introduces new exact solutions for null particles in (A)dS spaces by boosting known static solutions and extends to multiple particles and spinning null particles.

Findings

Null particles in (A)dS spaces are modeled by boosted solutions.

Ultrarelativistic BTZ black holes match boosted Deser-Jackiw solutions without angular momentum.

Multiple null particles can propagate simultaneously in the background.

Abstract

We obtain a class of exact solutions representing null particles moving in three-dimensional (anti-) de Sitter spaces by boosting the corresponding static point source solutions given by Deser and Jackiw. In de Sitter space the resulting solution describes two null particles moving on the (circular) cosmological horizon, while in anti-de Sitter space it describes a single null particle propagating from one side of the universe to the other. We also boost the BTZ black hole solution to the ultrarelativistic limit and obtain the solution for a spinning null particle moving in anti-de Sitter space. We find that the ultrarelativistic geometry of the black hole is exactly the same as that resulting from boosting the Deser-Jackiw solution when the angular momentum of the hole vanishes. A general class of solutions is also obtained which represents several null particles propagating in the Deser-Jackiw background. The differences between the three-dimensional and four-dimensional cases are also discussed.