Eikonal black hole ringings in generalized energy-momentum squared gravity

TL;DR

This paper explores how non-minimal matter-geometry coupling in generalized energy-momentum squared gravity affects black hole quasinormal modes, revealing deviations from the standard photon ring correspondence in the eikonal limit.

Contribution

It derives the coupled master equations for axial perturbations in charged black holes within this modified gravity model without assuming a specific action form.

Findings

The photon ring and quasinormal modes correspondence does not hold generally.

Axial perturbation fields propagate independently with different quasinormal frequencies.

Non-minimal coupling alters the standard black hole spectroscopy predictions.

Abstract

In the scope of black hole spectroscopy, several attempts have been made in the past decades in order to test black holes or gravitational theories via black hole quasinormal modes. In the eikonal approximation, the quasinormal modes are generically associated with the photon ring of the black hole. This correspondence is valid for most cases in general relativity, but may not be true in other theories of gravity. In this paper, we consider the generalized energy-momentum squared gravity in which matter fields are non-minimally coupled to geometry. We investigate the axial perturbations of the charged black holes in this model, without assuming any explicit expression of the action functional. After obtaining the modified Klein-Gordon equation and the modified Maxwell equations, we perturb the gravitational equations and the modified Maxwell equations to derive the coupled master equations of the axial perturbations. In the presence of the non-minimal coupling between matter and geometry, the correspondence between the eikonal quasinormal modes and the photon ring is not satisfied in general. Also, the two coupled fields of the axial perturbations are found to propagate independently and they do not share the same quasinormal frequencies in the eikonal limit.