Dynamical Henneaux-Teitelboim Gravity

TL;DR

This paper introduces a generalized gravity model called dynamical Henneaux-Teitelboim gravity, extending unimodular gravity with kinetic terms, and analyzes its solutions in spherically symmetric and cosmological contexts.

Contribution

It proposes a new dynamical extension of Henneaux-Teitelboim unimodular gravity with kinetic terms and explores its solutions analytically.

Findings

Derived approximate black hole solutions for small couplings.

Found approximate cosmological backgrounds by perturbing around de Sitter space.

Demonstrated the model's consistency with known solutions in specific regimes.

Abstract

We consider a modified gravity model which we call "dynamical Henneaux-Teitelboim gravity" because of its close relationship with the Henneaux-Teitelboim formulation of unimodular gravity. The latter is a fully diffeomorphism-invariant formulation of unimodular gravity, where full diffeomorphism invariance is achieved by introducing two additional non-dynamical fields: a scalar, which plays the role of a cosmological constant, and a three-form whose exterior derivative is the spacetime volume element. Dynamical Henneaux-Teitelboim gravity is a generalization of this model that includes kinetic terms for both the scalar and the three-form with arbitrary couplings. We study the field equations for the cases of spherically symmetric and homogeneous, isotropic configurations. In the spherically symmetric case, we solve the field equations analytically for small values of the coupling to obtain an approximate black hole solution. In the homogeneous and isotropic case, we perturb around de Sitter space to find an approximate cosmological background for our model.