Regge-Wheeler equation, linear stability, and greybody factors for dirty black holes

TL;DR

This paper derives general forms of the Regge-Wheeler equation and establishes bounds on greybody factors for 'dirty' black holes with non-zero surrounding stress-energy, extending stability analysis beyond vacuum cases.

Contribution

It provides the first general formulation of the Regge-Wheeler equation for various perturbations on arbitrary static spherically symmetric backgrounds with non-zero stress-energy.

Findings

Derived general Regge-Wheeler equations for spin 0, 1, and 2 perturbations.

Established rigorous bounds on greybody factors for dirty black holes.

Analyzed effects of stress-energy on black hole stability and properties.

Abstract

So-called "dirty" black holes are those surrounded by non-zero stress-energy, rather than vacuum. The presence of the non-zero stress-energy modifies key features of the black hole, such as the surface gravity, Regge-Wheeler equation, linear stability, and greybody factors in a rather nontrivial way. Working within the inverse-Cowling approximation, (effectively the test-field limit), we shall present general forms for the Regge-Wheeler equation for linearized spin 0, spin 1, and axial spin 2 perturbations on an arbitrary static spherically symmetric background spacetime. Using very general features of the background spacetime, (in particular the classical energy conditions for the stress-energy surrounding the black hole), we extract several interesting and robust bounds on the behaviour of such systems, including rigorous bounds on the greybody factors for dirty black holes.