Conformal Killing gravity in static spherically-symmetric spacetimes

Fuente: arXiv
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Main Authors: Mantica, Carlo Alberto, Molinari, Luca Guido
Format: Preprint
Published: 2024
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author Mantica, Carlo Alberto
Molinari, Luca Guido
author_facet Mantica, Carlo Alberto
Molinari, Luca Guido
contents We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$ for static spherically symmetric spacetimes, and write the conformal Killing gravity equations as Einstein equations augmented by this tensor. The field equations are of second order: this fact allows for analytic solutions and considerably simplifies the derivation of results of previous studies based on the original Harada equations. In particular, we prove the equivalence of the known third order field equations, with the second order ones obtained by us in the conformal Killing parametrization. The structure of the Ricci tensor and of the conformal Killing tensor are compatible with both anisotropic fluid sources and (non)-linear electrodynamics. We reobtain covariantly and in simple steps the general static spherical solutions for vacuum and linear electrodynamics. Moreover we recover the purely magnetic Lagrangian functions that induce metrics of interest for black holes.
format Preprint
id arxiv_https___arxiv_org_abs_2406_12511
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Conformal Killing gravity in static spherically-symmetric spacetimes
Mantica, Carlo Alberto
Molinari, Luca Guido
General Relativity and Quantum Cosmology
83D05 (Primary), 83C20 (Secondary)
We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$ for static spherically symmetric spacetimes, and write the conformal Killing gravity equations as Einstein equations augmented by this tensor. The field equations are of second order: this fact allows for analytic solutions and considerably simplifies the derivation of results of previous studies based on the original Harada equations. In particular, we prove the equivalence of the known third order field equations, with the second order ones obtained by us in the conformal Killing parametrization. The structure of the Ricci tensor and of the conformal Killing tensor are compatible with both anisotropic fluid sources and (non)-linear electrodynamics. We reobtain covariantly and in simple steps the general static spherical solutions for vacuum and linear electrodynamics. Moreover we recover the purely magnetic Lagrangian functions that induce metrics of interest for black holes.
title Conformal Killing gravity in static spherically-symmetric spacetimes
topic General Relativity and Quantum Cosmology
83D05 (Primary), 83C20 (Secondary)
url https://arxiv.org/abs/2406.12511