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

TL;DR

Problem addressed: characterization of null-particle spacetimes in three-dimensional (A)dS spaces. Method: apply ultrarelativistic boosts to DJ static point-particle solutions and to the BTZ black hole, supplemented by a coordinate-shift construction for null sources. Main results: in dS3 the boosted solution consists of two null particles on the cosmological horizon; in AdS3 a single null particle traverses the universe; the spinless BTZ boost reproduces the same ultrarelativistic geometry as DJ, while spin introduces an additional term; multi-particle DJ configurations are built via horizon patching. Significance: highlights the distinct global nature of 3D gravity, shows boost methods extend to (A)dS backgrounds, and clarifies differences from the four-dimensional case (e.g., absence of gravitons).

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.