Eikonal quasinormal modes of black holes beyond general relativity II: generalised scalar-tensor perturbations

TL;DR

This paper derives analytic formulas for the fundamental quasinormal modes of black holes in scalar-tensor theories beyond general relativity, incorporating scalar mass, derivative couplings, and rotation effects, to aid gravitational wave black hole spectroscopy.

Contribution

It extends previous work by providing a general, theory-agnostic eikonal approximation for coupled scalar-tensor perturbations, including scalar mass, derivative couplings, and rotational corrections.

Findings

Analytic formulas for quasinormal mode frequencies and damping rates in scalar-tensor theories.

Extension to rotating black holes with frame dragging effects.

Application to scalar wave equations in stationary-axisymmetric spacetimes.

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.