Conformal Killing gravity in static spherically-symmetric spacetimes

Abstract

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.

Final version (typos in eqs 19, 20 corrected)

References in corpus (4)

• Gravity at cosmological distances: Explaining the accelerating expansion without dark energy
• Black bounces in conformal Killing gravity
• Dark energy in conformal Killing gravity
• Friedmann equations in the Codazzi parametrization of Cotton and extended theories of gravity and the Dark Sector

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• Linearized Stability of Harada Thin-Shell Wormholes
• Note on conserved currents in static Conformal Killing Gravity
• Confronting dark energy in Harada's Conformal Killing Gravity with observational data
• Constraints on cosmological parameters and CMB first acoustic peak in conformal Killing gravity
• Generalized Vaidya Spacetime in Cotton and Conformal Killing Theories
• Thermodynamics and information recovery of Schwarzschild AdS black holes in conformal Killing gravity