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

We obtain a class of exact solutions representing null particles moving in three-dimensional (anti-) de Sitter spaces by boosting the corresponding st atic point source solutions given by Deser and Jackiw. In de Sitter space t he 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 al so boost the Banados-Teitelboim-Zanelli black hole solution to the ultrarel ativistic limit and obtain the solution for a spinning null particle moving in anti-de Sitter space. We find that the ultrarelativistic geometry of th e 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 c lass of solutions is also obtained which represents several null particles propagating in the Deser-Jackiw background. The differences between the thr ee-dimensional and four-dimensional cases are also discussed. (C) 1999 Amer ican Institute of Physics. [S0022-2488(99)03907-9].