General spherically symmetric solution of Cotton gravity

TL;DR

This paper derives the general spherically symmetric vacuum solution in Cotton gravity, revealing potential singularities that may prevent black hole formation and showing modifications to gravity that could explain dark energy.

Contribution

It provides the first general spherically symmetric static vacuum solution in Cotton gravity, highlighting its implications for black hole formation and cosmic acceleration.

Findings

Presence of singularities at the photosphere of spherical sources.

Potential obstruction to stellar black hole formation.

Long-range modifications to Newtonian gravity related to dark energy.

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.