Hairy Black Holes: Non-existence of Short Hairs and Bound on Light Ring Size

Abstract: Several hairy black hole solutions are known to violate the original version of the celebrated no-hair conjecture. This prompted the development of a new theorem that establishes a universal lower bound on the extension of hairs outside any $4$-dimensional black hole solutions of general relativity. Our work presents a novel generalization of this no-short hair'' theorem, which notably does not use gravitational field equations and is valid for arbitrary spacetime dimensions ($D \geq 4$). Consequently, irrespective of the underlying theory of gravity, thehairosphere'' must extend to the innermost light ring of the black hole spacetime. Various possible observational implications of this intriguing theorem are discussed, and other useful consequences are explored.