Statistical Origin of Black Hole Entropy in Induced Gravity
V. P. Frolov, D. V. Fursaev, A. I. Zelnikov
TL;DR
The paper shows that in induced gravity, gravity and black hole entropy can be understood as emergent from the statistical mechanics of heavy, Planck-scale constituents. By comparing the covariant effective action with a conical-singularity (off-shell) computation, it derives a precise decomposition $S^{BH}=S^{SM}-\sum_s 2\pi\xi_s \int_\Sigma d\sigma \langle \hat{\phi}^2_s\rangle$, with $S^{SM}$ identified as the statistical entropy of the heavy fields near the horizon. The main result asserts that $S^{BH}$ is the ultraviolet-finite, horizon-local contribution of constituent field statistics, while nonminimal couplings provide the necessary horizon terms. The work introduces the low-energy censorship conjecture, suggesting consistency with any ultraviolet completion (e.g., string theory) must reproduce the same $S^{BH}$ from low-energy gravity. The analysis emphasizes that BH entropy in these models originates from a Planck-scale near-horizon layer and is not merely the thermodynamic entropy of quantum excitations in the exterior region.
Abstract
The statistical-mechanical origin of the Bekenstein-Hawking entropy $S^{BH}$ in the induced gravity is discussed. In the framework of the induced gravity models the Einstein action arises as the low energy limit of the effective action of quantum fields. The induced gravitational constant is determined by the masses of the heavy constituents. We established the explicit relation between statistical entropy of constituent fields and black hole entropy $S^{BH}$.