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

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.

Higgs–Chern–Simons Gravity Models in d = 2n + 1 Dimensions

“…The present work, which is a continuation of that done in Ref. [6] for the the lowest dimension d = 3, provides the explicit expression of the HCS Lagrangians up to d = 7, together with an investigation of the simplest solutions for d = 3, 5. These solutions have the property that they do not backreact on the spacetime geometry in common, i.e., their effective energy-momentum tensor vanishes.…”

“…of the Einstein equations with negative cosmological constant vanishes (the analogy of these solutions with self-dual Yang-Mills instantons in a curved space geometry [15][16][17], was noticed in Ref. [6]. There, we dubbed these closed form solutions as effectively vacuum confiurations.…”

“…A preliminary investigation of the simplest solutions in d = 3, 5 dimensions is considered in Section 3, extending the study (for the n = 1 case) in Ref. [6]. Section 4 presents the concluding remarks.…”

“…Moreover, Ref. [6] has given arguments that (at least in the c 1 = c 2 limit), solutions (30) and (31) appear to be unique. Because the discussion here in d = 3 is similar to that in the d = 5 case, we restrict to the discussion of the latter, as below.…”

“…Following the Ref. [6], let us briefly review this construction. As discussed there, the expression of the new-CS densities is found following exactly the same method as the usual-CS densities in odd dimensions.…”