Tolman-Oppenheimer-Volkoff equation and static spheres in Conformal Killing gravity

TL;DR

This paper derives a modified Tolman-Oppenheimer-Volkoff equation within conformal Killing gravity, revealing new dark terms and enabling analysis of static spheres with anisotropic matter in this alternative gravity framework.

Contribution

It introduces a novel TOV equation in conformal Killing gravity, incorporating dark terms and extending Buchdahl's critical radius analysis for anisotropic fluids.

Findings

Derived the conformal Killing gravity TOV equation with dark terms.

Solved for a perfect fluid sphere with uniform density in Harada vacuum.

Extended Buchdahl's critical radius relation in this gravity context.

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.