Chern--Simons Gravity from 3+1 Dimensional Gravity

Details Chern--Simons Gravity from 3+1 Dimensional Gravity Chern--Simons Gravity from 3+1 Dimensional Gravity

1992-11-03

arxiv.org/abs/gr-qc/9211001v2

Phys.Lett. B300 (1993) 38-43

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages (TeX manuscript)

Scientific paper

10.1016/0370-2693(93)90745-4

In the context of a Poincar\'e gauge theoretical formulation, pure gravity in 3+1-dimensions is dimensionally reduced to gravity in 2+1-dimensions with or without cosmological constant $\Lambda$. 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 $\Lambda\le 0$ (in particular the black-hole solution recently found by Banados, Teitelboim and Zanelli) and those of 1+1-dimensional Liouville gravity, are thus mapped into 3+1-dimensional vacuum solutions.

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