Perturbations of a Schwarzschild black hole in torsion bigravity

TL;DR

This paper analyzes linear perturbations of Schwarzschild black holes within torsion bigravity, demonstrating stability conditions, decoupled equations for excitations, and exploring quasi-bound states and superradiance effects.

Contribution

It extends stability analysis to non-spherical perturbations in torsion bigravity and characterizes the structure of perturbation equations and conditions for avoiding singularities.

Findings

Linear stability holds for all multipolarities L ≥ 1 if ppa r_h > \u221a(1+ta).

Perturbation equations have a triangular structure with decoupled massive spin-2 modes.

Explicit complex quasi-bound frequencies are computed, and superradiance instability is briefly discussed.

Abstract

In this paper we pursue the study of linear perturbations around a Schwarzschild black hole in a generalized Einstein-Cartan theory of gravity, called torsion bigravity. This theory contains both massless and massive spin-2 excitations. Here we consider non spherically-symmetric perturbations with generic multipolarity $L \geq 1$. We extend the conclusion of linear stability, previously obtained for $L=0$ [Phys. Rev. D 104, 024032], to the generic $L \geq 1$ case. We prove that the mass $\kappa$ of the massive spin-2 excitation must be large enough, namely $\kappa r_h > \sqrt{1+\eta}$, to avoid the presence of singularities in the perturbation equations. The perturbation equations are shown to have a triangular structure, where massive spin-2 excitations satisfy decoupled equations, while the Einstein-like massless spin-2 ones satisfy inhomogeneous equations sourced by the massive spin-2 sector. We study quasi-bound states, and exhibit some explicit complex quasi-bound frequencies. We briefly discuss the issue of superradiance instabilities.