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.

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• Alternative gravity theories
• General relativity