Chern-Simons gravity from (3 + 1)-dimensional gravity

Abstract

In the context of a Poincaré gauge theoretical formulation, pure gravity in 3 + 1 dimensions is dimensionally reduced to gravity in 2 + 1 dimensions with or without cosmological constant Λ. The dimensional reductions are consistent with the gauge symmetries, mapping ISO (3, 1) gauge transformations into ISO (2, 1) ones. One of the reductions leads to Chern-Simons-Witten gravity. The solutions of 2 + 1 gravity with Λ⩽0 (in particular the black-hole solution recently found by Banados, Teitelboim and Zanelli) and those of (1 + 1)-dimensional Liouille gravity, are thus mapped into (3 +1)-dimensional vacuum solutions.