Abstract: 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 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 Liouville gravity, are thus mapped into 3+1-dimensional vacuum solutions.
Nardelli, G., Grignani, G., Chern-Simons gravity from (3+1)-dimensional gravity, <<PHYSICS LETTERS. SECTION B>>, 1993; (300): 38-43. [doi:10.1016/0370-2693(93)90745-4] [http://hdl.handle.net/10807/7889]
Chern-Simons gravity from (3+1)-dimensional gravity
Nardelli, Giuseppe;Grignani, Gianluca
1993
Abstract
Abstract: 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 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 Liouville gravity, are thus mapped into 3+1-dimensional vacuum solutions.
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