Exact Absolute Zero via Black Hole Negative Heat Capacity: A Deductive Consequence of Quantum Thermodynamics and General Relativity

We prove that exact absolute zero is not forbidden by the laws of physics. The Masanes-Oppenheim theorem: the definitive derivation of the third law of thermodynamics, states that perfect cooling in finite time is possible if and only if the heat capacity of the thermal bath is not positive. Schwarzschild black holes possess negative heat capacity, C = -8πM² < 0, a generic property of all self‑gravitating systems. We construct an idealised cooling protocol: a quantum system is placed in thermal contact with a Schwarzschild black hole; as the system transfers energy to the black hole, the black hole's temperature decreases, maintaining a finite temperature gradient that allows the system to drain all its entropy in finite time and reach its exact ground state. We demonstrate that the third law of black hole mechanics, which constrains the black hole's own temperature, does not apply to its use as a reservoir for another system, and that recent results have demonstrated its violation in vacuum gravity. We further show that analogue black holes in Bose-Einstein condensates provide a laboratory pathway toward testing the negative heat capacity cooling mechanism. The logical conjunction of the Masanes-Oppenheim theorem and black hole thermodynamics yields a deductive proof that exact absolute zero is permitted by the known laws of physics, resolving the paradox that has persisted since the escape clause was first articulated in 2017.