Teukolsky-like equations with various spins in a deformed Kerr spacetime

TL;DR

This paper derives unified Teukolsky-like wave equations for various spins in a deformed Kerr spacetime, analyzing their structure and singularities to facilitate gravitational-wave studies.

Contribution

It provides a unified formulation of wave equations with different spins in a deformed Kerr background, simplifying analysis and understanding of their singularity structure.

Findings

Unified Teukolsky-like equations for various spins derived

Simplification achieved using a separable gauge

Analysis of singularities and solution behavior around them

Abstract

We study the wave equations with the various spins on the background of the Kerr metric deformed by a function of the radial coordinate, on which background we have studied the gravitational-wave equations previously. We obtain the unified expression of the Teukolsky-like master equations and the corresponding radial equations with various spins. We find that taking the separable gauge introduced in previous study simplifies the unified form. We also discuss the structure of the radial equation as an ordinary differential equation, such as the existence of the regular and the irregular singularities of the equation and the behavior of the solution around each singularity.