Black hole entropy contributions from Euclidean cores

The entropy of a Schwarzschild black hole, as computed via the semiclassical Euclidean path integral in a stationary phase approximation, is determined not by the on-shell value of the action (which vanishes), but by the Gibbons--Hawking--York boundary term evaluated on a suitable hypersurface, which can be chosen arbitrarily far away from the horizon. For this reason, the black hole singularity seemingly has no influence on the Bekenstein--Hawking area law. In this Essay we estimate how a regular black hole core, deep inside a Euclidean black hole of mass $M$ and generated via a UV regulator length scale $\ell>0$, affects the black hole entropy. The contributions are suppressed by factors of $\ell/(2GM)$; demanding exact agreement with the area law as well as a self-consistent first law of black hole thermodynamics at all orders, however, demands that these contributions vanish identically via uniformly bounded curvature. This links the limiting curvature hypothesis to black hole thermodynamics.