Second-law check through the inner Cauchy horizon of regular black holes with nonlocal fakeon-regulated mass inflation

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Regular black holes—those without a central singularity—have an inner horizon inside the event horizon. When a regular black hole is slightly disturbed, a process called mass inflation causes the energy density near the inner horizon to grow exponentially, which would normally destabilize the spacetime. A new theoretical tool called the “fakeon” regulator, derived from a nonlocal theory of gravity, tames this divergence, allowing the inner horizon to survive generic perturbations. The authors use one specific version of this regulator (labeled S3) to study whether the black hole’s total entropy always increases over time, as required by the second law of thermodynamics. The total entropy is taken as the sum of the Bekenstein–Hawking area entropies of both horizons, plus small corrections from the nonlocal theory. As the black hole evolves, the outer horizon’s area grows while the inner horizon’s area shrinks, making the sign of the total entropy change non‑trivial. The researchers find that, for a wide range of black hole masses (including nearly extremal cases) and for different decay rates of the perturbation, the inner horizon’s negative contribution is always small enough that the total entropy never decreases. This result holds to machine precision in every test performed. The other version of the regulator (S4) requires a separate analysis and is not covered here. Overall, the study shows that the second law can be satisfied even when mass inflation is regulated by a nonlocal fakeon mechanism, supporting the consistency of such theories with black hole thermodynamics.

AI-generated (deepseek-v4-flash) · created 2026-05-21