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

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.