Spherically symmetric perturbations of a Schwarzschild black hole in torsion bigravity

TL;DR

This paper investigates the stability of Schwarzschild black holes under spherically symmetric perturbations within torsion bigravity, revealing conditions for avoiding singularities and confirming linear stability.

Contribution

It derives a Zerilli-like equation for perturbations in torsion bigravity and establishes stability criteria for Schwarzschild black holes.

Findings

Perturbations reduce to a Zerilli-like equation.

Singularity avoidance restricts spin-2 mass range.

Schwarzschild black holes are linearly stable.

Abstract

Time-dependent spherically-symmetric perturbations of Schwarzschild black holes are studied within torsion bigravity, i.e., within generalized Einstein-Cartan theories where the dynamical torsion carries massive spin-2 excitation. We reduce linearized perturbations to a Zerilli-like equation. The structure of the potential entering the latter Zerilli-like equation has two important consequences. First, in order to avoid the presence of singularities in generic perturbations, one must restrict the range (or inverse mass) of the spin-2 excitation to be (essentially) smaller than the radius of the considered black hole. Second, we then show that the Schwarzschild black hole is linearly stable against spherically-symmetric perturbations.