Linearized gravity and gauge conditions

TL;DR

This paper derives decoupled field equations for linearized gravity and other integer spin fields on Kerr and Petrov type D spacetimes using GHP formalism, generalizing known equations like Regge-Wheeler and Zerilli.

Contribution

It provides a systematic derivation of gauge-invariant equations for linearized fields on complex spacetimes, extending previous results to more general gauge conditions and backgrounds.

Findings

Decoupled equations for all spin weights derived using GHP formalism

Generalized harmonic gauge leads to a generalized Regge-Wheeler equation

Special case yields gauge-invariant Regge-Wheeler and Zerilli equations

Abstract

In this paper we consider the field equations for linearized gravity and other integer spin fields on the Kerr spacetime, and more generally on spacetimes of Petrov type D. We give a derivation, using the GHP formalism, of decoupled field equations for the linearized Weyl scalars for all spin weights and identify the gauge source functions occuring in these. For the spin weight 0 Weyl scalar, imposing a generalized harmonic coordinate gauge yields a generalization of the Regge-Wheeler equation. Specializing to the Schwarzschild case, we derive the gauge invariant Regge-Wheeler and Zerilli equation directly from the equation for the spin 0 scalar.