Black Hole Entropy and Gravity Cutoff

TL;DR

The paper tackles the puzzle that black hole entropy, when viewed as entanglement entropy, seemingly depends on the number of species $N$. It argues that the correct gravitational UV cutoff shrinks with $N$ as $\Lambda = M_{ m Planck}/\sqrt{N}$, and that using this cutoff makes the entanglement entropy $S_{\rm ent} = N\Lambda^2 A(\Sigma)$ coincide with the universal BH entropy $S_{BH} = M^2_{\rm Pl} A(\Sigma)$ in explicit fundamental-theory scenarios. Through high-dimensional KK/torus compactifications and AdS/CFT (RS brane) examples, the authors show consistent equality $S_{\rm ent}=S_{BH}$ across regimes and representations, supporting a universal resolution to the species problem. The work highlights the significance of the gravity cutoff in reconciling statistical and geometric perspectives on black hole entropy and suggests extensions to arbitrary dimensions and string-theoretic settings.

Abstract

We study the black hole entropy as entanglement entropy and propose a resolution to the species puzzle. This resolution comes out naturally due to the fact that in the presence of $N$ species the universal gravitational cutoff is $Λ=M_{\rm Planck}/\sqrt{N}$, as opposed to $M_{\rm Planck}$. We demonstrate consistency of our solution by showing the equality of the two entropies in explicit examples in which the relation between $M_{\rm Planck}$ and $Λ$ is known from the fundamental theory.