Vanishing of Conserved Charges in Cotton Gravity

TL;DR

Cotton gravity, a higher derivative extension of General Relativity, results in all solutions having zero conserved charges, raising questions about its physical viability or indicating a confinement mechanism.

Contribution

This paper demonstrates that all solutions in Cotton gravity, including black holes, have vanishing conserved charges, a novel and surprising property of the theory.

Findings

All solutions have zero mass and angular momentum.

Black holes in Cotton gravity carry no conserved charges.

The theory may be unphysical or exhibit confinement of energy.

Abstract

Cotton gravity was recently introduced as a higher derivative extension of General Relativity. The field equations of the theory involve the rank-3 Cotton tensor. Here we show that all solutions of the theory, including the black holes, have vanishing conserved charges, i.e. mass and angular momentum. This result implies that either the theory is unphysical since all the black holes carry the charges of the vacuum and can be created at no energy cost, or the theory has confinement of mass/energy and all other conserved quantities.