A perturbative infrared deformation of general relativity, with coefficients fixed by matching, reproduces the proposed third-law-compatible black hole entropy, and the same formula extends to Kerr-Newman black holes through the irreducible mass.
Black Holes with a Generalized Gravitational Action
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Microscopic black holes are sensitive to higher dimension operators in the gravitational action. We compute the influence of these operators on the Schwarzschild solution using perturbation theory. All (time reversal invariant) operators of dimension six are included (dimension four operators don't alter the Schwarzschild solution). Corrections to the relation between the Hawking temperature and the black hole mass are found. The entropy is calculated using the Gibbons-Hawking prescription for the Euclidean path integral and using naive thermodynamic reasoning. These two methods agree, however, the entropy is not equal to 1/4 the area of the horizon.
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Information--Theoretic Black Hole Entropy II: Infrared Gravity and Charged/Rotating Extensions
A perturbative infrared deformation of general relativity, with coefficients fixed by matching, reproduces the proposed third-law-compatible black hole entropy, and the same formula extends to Kerr-Newman black holes through the irreducible mass.