Black hole entropy bounded by the specific heat

Black holes aren't just cold graves of gravity -- they have temperature and entropy. Previous studies have emphasized black holes' role as the most entropic objects in the universe, that the entropy of a region of space is bounded above by the area that encloses it. This work instead suggests a thermodynamic constraint, that black hole entropy is bounded above by their specific heat. The bound is rigorously proven for some symmetric, static cases and checked on spinning and charged ones. The conjecture turns a stability diagnostic -- specific heat -- into a universal ceiling on disorder, hinting at new links between geometry and thermodynamics.