Universal Bounds on Black Hole Observables Imposed by Energy Conditions

Abstract

We establish a universal connection between the classical energy conditions and directly observable black hole properties. By imposing the energy conditions locally at the photon sphere, we derive analytic and testable bounds on the shadow size, Lyapunov exponent, Lyapunov time, and photon-ring time delay that apply to all static, spherically symmetric black holes in General Relativity. Expressed equivalently in terms of either the spacetime metric functions or the local components of the stress-energy tensor, these bounds provide complementary tests of strong-field gravity that are independent of any specific black hole solution or matter model. They are directly applicable to current and forthcoming horizon-scale observations, constrain both admissible black hole spacetimes and their underlying matter sources, and establish the classical energy conditions as observational probes of strong-field gravity. Any observational violation of these bounds would signal either a violation of the classical energy conditions by the matter fields or a breakdown of General Relativity in the strong-field regime.