Teukolsky-like equations in a non-vacuum axisymmetric type D spacetime

Author:

Ya Guo, Hiroaki Nakajima, Wenbin Lin

Keyword:

General Relativity and Quantum Cosmology, General Relativity and Quantum Cosmology (gr-qc), High Energy Astrophysical Phenomena (astro-ph.HE)

journal:

date:

2023-09-11 16:00:00

Abstract

We study an axisymmetric metric satisfying the Petrov type D property with some additional ansatze, but without assuming the vacuum condition. We find that our metric in turn becomes conformal to the Kerr metric deformed by one function of the radial coordinate. We then study the gravitational-wave equations on this background metric in the case that the conformal factor is unity. We find that under an appropriate gauge condition, the wave equations admit the separation of the variables, and the separated equation for the radial coordinate gives a natural extension of the Teukolsky equation.

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