Hairy black holes: non-existence of short hairs and bound on light ring size

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≥4). Consequently, irrespective of the underlying theory of gravity, the ``hairosphere'' 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.