Perturbation theory of spherically symmetric self-similar black holes

TL;DR

This paper develops a perturbation theory for spherically symmetric self-similar black holes using the Newman-Penrose formalism, deriving separable wave equations for various fields and generalizing the Teukolsky equation.

Contribution

It introduces a generalized Teukolsky equation and analyzes monopole and dipole modes for self-similar black holes, expanding perturbation analysis methods.

Findings

Wave equations are separable but not decoupled.

Generalized Teukolsky equation is derived.

Monopole and dipole modes are explicitly treated.

Abstract

The theory of perturbations of spherically symmetric self-similar black holes is presented, in the Newman-Penrose formalism. It is shown that the wave equations for gravitational, electromagnetic, and scalar waves are separable, though not decoupled. A generalization of the Teukolsky equation is given. Monopole and dipole modes are treated. The Newman-Penrose wave equations governing polar and axial spin-0 perturbations are explored.