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.

9 pages, 7 figures. New section on vacuum solutions. Extension of TOV equation and junction conditions to anisotropic matter fluid. New figures. Text improved

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• Black Hole Thermodynamics in Harada's inspired theory of gravity: Stability, Phase Structure and Geometrothermodynamics
• 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
• The spacetime geodesy of perfect fluid spheres
• Thermodynamic formulation of Cotton gravity in the Codazzi parametrization