Match the logarithmic entropy correction of non-extremal black holes microscopically
In plain words
Beyond the area law, quantum effects add a small correction proportional to the logarithm of the area, with a coefficient that gravity alone determines. Any correct microscopic count must reproduce this number.
Precise statement
One-loop Euclidean gravity gives $S = A c^{3}/(4 G \hbar) + C \operatorname{ln}(A/\ell_{P}^{2}) + ...$, with $C$ fixed by the massless spectrum and the ensemble; Sen (2012) computed $C$ for Schwarzschild and Kerr in various dimensions. Reproduce $C$ from a microscopic count for a non-extremal black hole in some UV-complete theory. An answer is a microscopic derivation of $C$ agreeing with the macroscopic value.
What would settle it
A microscopic computation of the logarithmic coefficient for a non-BPS black hole that agrees with the one-loop gravity result.
Status in the literature
Unverified note
Macroscopic coefficients are known since 2012; microscopic matches exist only for BPS black holes as of 2026.