Stability analysis of Schwarzschild black holes in dynamical Chern-Simons gravity

TL;DR

This paper investigates the stability of Schwarzschild black holes within dynamical Chern-Simons gravity, revealing that despite parity violation, these black holes remain linearly stable under perturbations involving a massive scalar field.

Contribution

It demonstrates the linear mode stability of Schwarzschild black holes in dynamical Chern-Simons gravity, accounting for parity-violating effects and scalar field coupling.

Findings

Schwarzschild spacetime is an exact solution in dynamical Chern-Simons gravity.

Perturbations lead to coupled Schrödinger-like equations for metric and scalar fields.

Linear mode stability is proven for a generic massive scalar field.

Abstract

Dynamical Chern-Simons gravity has an interesting feature that the parity violating term exists, and the coupling is determined by a dynamical scalar field. When the spacetime has spherical symmetry, the parity violating term vanishes, and then the metric of the Schwarzschild spacetime with vanishing scalar field is an exact solution of dynamical Chern-Simons gravity. The effect of the Chern-Simons coupling appears in the study of perturbation around the Schwarzschild spacetime. Due to the parity violating term, the odd parity metric perturbation and the perturbed scalar field are coupled, and the perturbed field equations take the form of the coupled system of the Schr\"odinger equations. We prove linear mode stability for a generic massive scalar.