Eikonal quasinormal modes of black holes beyond general relativity. II. Generalized scalar-tensor perturbations

Abstract

Black hole 'spectroscopy', i.e. the identification of quasinormal mode frequencies via gravitational wave observations, is a powerful technique for testing the general relativistic nature of black holes. In theories of gravity beyond general relativity perturbed black holes are typically described by a set of coupled wave equations for the tensorial field and the extra scalar/vector degrees of freedom, thus leading to a theory-specific quasinormal mode spectrum. In this paper we use the eikonal/geometric optics approximation to obtain analytic formulae for the frequency and damping rate of the fundamental quasinormal mode of a generalised, theory-agnostic system of equations describing coupled scalar-tensor perturbations of spherically symmetric black holes. Representing an extension of our recent work, the present model includes a massive scalar field, couplings through the field derivatives and first-order frame-dragging rotational corrections. Moving away from spherical symmetry, we consider the simple model of the scalar wave equation in a general stationary-axisymmetric spacetime and use the eikonal approximation to compute the quasinormal modes associated with equatorial and nonequatorial photon rings. * hosilva@illinois.edu † kostas@um.es

Black hole gravitational waves in the effective field theory of gravity

“…[39] for a review). In this section, we shall follow the method developed in [40][41][42][43] and compute the leading corrections on the quasinormal frequency caused by the higherdimensional operators. The idea of this method is to make use of the asymptotical flatness of the background solution to parametrize the EFT corrections that they enter master equations (2.18) as a power-law expansion of the form…”

Gravitational ringing of rotating black holes in higher-derivative gravity

“…In order to compute all of these coefficients, we have performed a numerical integration of Eqs. ( 46), ( 42) and ( 49)- (50). This allows us to obtain the fundamental QNM frequencies for a range of values of χ and the corresponding coupling, λ ev or λ odd .…”

“…Here we show the higher-derivative contributions to the effective potentials in equations ( 43) and (47), as well as the coupling terms in ( 49)- (50).…”

“…The corrections to the QNM frequencies of nonrotating black holes have been obtained in a number of theories, including dynamical Chern-Simons gravity [38,39], Einstein-dilaton-Gauss-Bonnet gravity [40,41], and theories with quartic [33,42] and cubic [18] curvature terms, among other models [43][44][45][46]. In addition, theoryindependent approaches were studied in [42,47,48], while eikonal QNMs beyond GR were investigated in [49][50][51].…”

Effective Field Theory for the perturbations of a slowly rotating black hole

“…(3) A third approach is to parametrize the deviations from general relativistic expectations in a model-independent way. This can take the form of a phenomenological parametrization such as [27][28][29][30][31][32], or a parametrization at the level of the action governing the dynamics of black hole perturbations [33][34][35][36][37]. It is the last approach that is the subject of this paper.…”