Tolman-Oppenheimer-Volkoff equation and static spheres in Conformal Killing gravity
Abstract
We derive the analog of the Tolman - Oppenheimer - Volkoff equation in conformal Killing gravity in a static spherically symmetric spacetime, sourced by anisotropic fluid matter. It differs from the original equation by new dark terms associated to a conformal Killing tensor. The formulation of gravity as an Einstein equation augmented by a conserved conformal Killing tensor enables to implement the junction conditions for a sphere of anisotropic fluid with the conformal Killing vacuum. The equations are solved for a perfect fluid sphere with uniform matter density, in the Harada vacuum. The extension of Buchdahl's equation for the critical radius - mass density is obtained.
Keywords
Cite
@article{arxiv.2409.18663,
title = {Tolman-Oppenheimer-Volkoff equation and static spheres in Conformal Killing gravity},
author = {Carlo Alberto Mantica and Luca Guido Molinari},
journal= {arXiv preprint arXiv:2409.18663},
year = {2025}
}
Comments
9 pages, 7 figures. New section on vacuum solutions. Extension of TOV equation and junction conditions to anisotropic matter fluid. New figures. Text improved