Stability and Quasinormal Modes of Black holes in Tensor-Vector-Scalar theory: Scalar Field Perturbations

TL;DR

This paper investigates the stability and quasinormal mode spectrum of black holes in Tensor-Vector-Scalar (TeVeS) theory, revealing stability under scalar perturbations and how the spectrum deviates from General Relativity predictions based on the theory's parameters.

Contribution

It is the first study of scalar field quasinormal modes in TeVeS black holes, showing stability and quantifying spectrum deviations from GR as a function of coupling parameters.

Findings

Black holes in TeVeS are stable to scalar perturbations.

The QNM spectrum approaches 1/√2 times the GR scalar spectrum as coupling parameters tend to zero.

The spectrum varies by a few percent for larger coupling parameters.

Abstract

The imminent detection of gravitational waves will trigger precision tests of gravity through observations of quasinormal ringing of black holes. While General Relativity predicts just two polarizations of gravitational waves, the so-called plus and cross polarizations, numerous alternative theories of gravity predict up to six different polarizations which will potentially be observed in current and future generations of gravitational wave detectors. Bekenstein's Tensor-Vector-Scalar (TeVeS) theory and its generalization fall into one such class of theory that predict the full gamut of six polarizations of gravitational waves. In this paper we begin the study of quasinormal modes (QNMs) in TeVeS by studying perturbations of the scalar field in a spherically symmetric background. We show that, at least in the case where superluminal propagation of perturbations is not present, black holes are generically stable to this kind of perturbation. We also make a unique prediction that, as the limit of the various coupling parameters of the theory tend to zero, the QNM spectrum tends to $1/\sqrt{2}$ times the QNM spectrum induced by scalar perturbations of a Schwarzschild black hole in General Relativity due to the intrinsic presence of the background vector field. We further show that the QNM spectrum does not vary significantly from this value for small values of the theory's coupling parameters, however can vary by as much as a few percent for larger, but still physically relevant parameters.