A Higgs--Chern-Simons gravity model in 2+1 dimensions

TL;DR

This paper introduces a new Higgs-Chern-Simons gravity model in 2+1 dimensions, constructs a black hole solution generalizing BTZ, and analyzes its thermodynamic properties compared to the standard BTZ black hole.

Contribution

It presents the first application of Higgs-Chern-Simons densities to 2+1 dimensional gravity, deriving new black hole solutions from higher-dimensional topological densities.

Findings

Constructed a closed-form black hole solution generalizing BTZ.

Analyzed thermodynamics of the new black hole and compared with BTZ.

Extended the model to include electric charge via Maxwell term.

Abstract

We study a gravity model in 2+1 dimensions, arising from a generalized Chern-Simons (CS) density we call a Higgs-Chern-Simons (HCS) density. This generalizes the construction of gravitational systems resulting from non-Abelian CS densities in all odd dimensions. The new HCS densities employed here are arrived at by the usual one-step descent of new Higgs--Chern-Pontryagin (HCP) densities, the latter resulting from the dimensional reduction of Chern-Pontryagin (CP) densities in some even dimension, such that in any given dimension (including even) there is an infinite tower of such models. Here, we restrict our attention to the lowest dimension, 2+1, and to the simplest such model resulting from the dimensional reduction of the $3$-rd CP density. We construct a black hole (BH) solution in closed form, generalizing the familiar BTZ BH. We also study the electrically charged BH solution of the same model augmented with a Maxwell term, and contrast this solution with the electrically charged BTZ BH, specifically concering their respective thermodynamic properties.