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Chern--Simons Gravity from 3+1 Dimensional Gravity

G. Grignani·G. Nardelli
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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 $Λ\le 0$ (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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G. Grignani, G. Nardelli. 1992-11-09. Chern--Simons Gravity from 3+1 Dimensional Gravity. https://doi.org/10.1016/0370-2693(93)90745-4

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