General spherically symmetric solution of Cotton gravity

Abstract

In this paper we present the general spherically symmetric static solution to the vacuum equations of Cotton gravity. The obtained metric solution reveals the presence of singularities at the photosphere of a spherical source, which probably obstruct the formation of the stellar Schwarzschild-radius black holes. The solution is characterized by two integration constants, whose values can be restricted by association with the Hubble horizon. We examine the diverse features of the solution, including the long-range modifications to Newton's force through the incorporation of the velocity-squared repulsive term to model the dark energy.

Journal version

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• Vanishing of Conserved Charges in Cotton Gravity
• Constrain the linear scalar perturbation theory of Cotton gravity
• Testing Cotton gravity as dark matter substitute with weak lensing
• Black hole solutions in Cotton gravity coupled to nonlinear electrodynamics
• Schouten-Codazzi Gravity
• Constraints on the $\gamma$-parameter for the vacuum solution of Cotton gravity with geodesics and shadows
• Generalized Vaidya Spacetime in Cotton and Conformal Killing Theories