The Black Hole as the Darkest Object: An Information-Theoretic No-Hair Theorem

In any quantum theory with dynamical gravity, a spatially localized system is inevitably coupled to its environment through the gravitational field. We prove that this coupling forces a non‑zero minimum of accessible classical information: an external observer can always extract at least the information encoded in the asymptotic conserved charges (mass, angular momentum, electric charge). We formulate this as a lower bound on the classical capacity of the gravitational channel from the interior to future null infinity. For a stationary black hole, the celebrated no‑hair theorem implies that this bound is saturated: a black hole leaks exactly the charges and no additional information about its internal state. Thus, a black hole is the darkest possible object compatible with gravity—it realizes the fundamental minimum of information leakage. The result connects the no‑hair theorem with quantum information theory and offers a new perspective on the black hole information paradox.