Maxwell Chern-Simons gravity in 3D: Thermodynamics of cosmological solutions and black holes with torsion

TL;DR

This paper explores three-dimensional Maxwell Chern-Simons gravity with torsion, establishing boundary conditions, analyzing solutions like cosmological spacetimes and black holes, and deriving their thermodynamic properties including a novel entropy formula.

Contribution

It introduces generalized asymptotic conditions for Maxwell Chern-Simons gravity with torsion and derives thermodynamics for new solutions with spin-2 charges.

Findings

Existence of solutions with mass, angular momentum, and spin-2 charge.

Black hole solutions with torsion generalize BTZ geometries.

A new entropy formula involving horizon area and spin-2 fields.

Abstract

We construct generalized sets of asymptotic conditions for both three-dimensional Maxwell Chern-Simons gravity and a novel extension that incorporates torsion through a deformation of the Maxwell algebra. These boundary conditions include the most general temporal components of the gauge fields that consistently preserve the corresponding asymptotic Maxwell algebras with identical classical central charges, while allowing for the inclusion of chemical potentials conjugate to the conserved charges. We show that both sets of asymptotic configurations admit nontrivial solutions carrying not only mass and angular momentum but also an additional global spin-2 charge. In the torsionless case, the theory admits locally flat cosmological spacetimes, whereas in the presence of torsion, it generalizes to BTZ-like black hole geometries. For each case, the thermodynamic properties are consistently derived in terms of the gauge fields and the topology of the Euclidean manifold, shown to correspond to a solid torus. Furthermore, we obtain a general expression for the entropy, depending on both the horizon area and its spin-2 analogues, which can be written as a reparametrization-invariant integral of the induced spin-2 fields on the spacelike section of the horizon.