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

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