Quasinormal modes of black holes encircled by a gravitating thin disk

TL;DR

This study investigates how a gravitating thin disk around a Schwarzschild black hole affects its quasinormal modes, revealing frequency shifts and potential universal relations that could impact black hole spectroscopy.

Contribution

It introduces a first-order analysis of disk effects on black hole QNMs, highlighting frequency shifts and a possible universal relation in the presence of a thin disk.

Findings

Disk presence decreases QNM frequencies and decay rates.

A potential universal relation for QNM frequencies in disk-affected black holes.

Discussion of QNMs in the eikonal limit and photon orbit correspondence.

Abstract

The ringdown phase of gravitational waves emitted by a perturbed black hole is described by a superposition of exponentially decaying sinusoidal modes, called quasinormal modes (QNMs), whose frequencies depend only on the property of the black hole geometry. The extraction of QNM frequencies of an isolated black hole would allow for testing how well the black hole is described by general relativity. However, astrophysical black holes are not isolated. It remains unclear whether the extra matter surrounding the black holes such as accretion disks would affect the validity of the black hole spectroscopy when the gravitational effects of the disks are taken into account. In this paper, we study the QNMs of a Schwarzschild black hole superposed with a gravitating thin disk. Considering up to the first order of the mass ratio between the disk and the black hole, we find that the existence of the disk would decrease the oscillating frequency and the decay rate. In addition, within the parameter space where the disk model can be regarded as physical, there seems to be a universal relation that the QNM frequencies tend to obey. The relation, if it holds generically, would assist in disentangling the QNM shifts caused by the disk contributions from those induced by other putative effects beyond general relativity. The QNMs in the eikonal limit, as well as their correspondence with bound photon orbits in this model, are briefly discussed.