Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes

Fuente: arXiv
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Hauptverfasser: Gray, Finnian, Kubiznak, David
Format: Preprint
Veröffentlicht: 2024
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_version_ 1866913416149467136
author Gray, Finnian
Kubiznak, David
author_facet Gray, Finnian
Kubiznak, David
contents It is well known that the Kerr--NUT--AdS spacetimes possess hidden symmetries encoded in the so-called principal Killing--Yano tensor. In this paper, focusing on the four-dimensional case, we obtain a number of symmetry operators for scalar, vector, and tensor perturbations, that are of degree two (to be defined below) and homogeneous in the principal tensor. In particular, by considering homogeneous operators that are linear, quadratic, and cubic in the principal tensor, we recover a complete set of 4 mutually commuting operators for scalar perturbations, underlying the separability of (massive) scalar wave equation. Proceeding to vector and tensor perturbations of the Kerr--NUT--AdS spacetimes, we find a set of 7 and 8 commuting operators, respectively. It remains to be seen whether such operators can be used to separate the corresponding spin 1 and spin 2 test field equations in these spacetimes.
format Preprint
id arxiv_https___arxiv_org_abs_2401_03553
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes
Gray, Finnian
Kubiznak, David
General Relativity and Quantum Cosmology
High Energy Physics - Theory
It is well known that the Kerr--NUT--AdS spacetimes possess hidden symmetries encoded in the so-called principal Killing--Yano tensor. In this paper, focusing on the four-dimensional case, we obtain a number of symmetry operators for scalar, vector, and tensor perturbations, that are of degree two (to be defined below) and homogeneous in the principal tensor. In particular, by considering homogeneous operators that are linear, quadratic, and cubic in the principal tensor, we recover a complete set of 4 mutually commuting operators for scalar perturbations, underlying the separability of (massive) scalar wave equation. Proceeding to vector and tensor perturbations of the Kerr--NUT--AdS spacetimes, we find a set of 7 and 8 commuting operators, respectively. It remains to be seen whether such operators can be used to separate the corresponding spin 1 and spin 2 test field equations in these spacetimes.
title Homogeneous Symmetry Operators in Kerr--NUT--AdS Spacetimes
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
url https://arxiv.org/abs/2401.03553