Dynamical Black-Hole Entropy: One Ledger, Many Schedules
Year: 2026
Type: preprint
Abstract: : All admissible dynamical black-hole entropy prescriptions at four derivatives share a single normalized retardation kernel, K(s)=κe−κsK(s)=\kappa e^{-\kappa s} K(s)=κe−κs. Its zeroth moment - - equal to unity, and forced by the identity of the underlying booking operators - carries the invariant total (one ledger); its first moment, 1/κ1/\kappa 1/κ plus prescription-specific clock shifts, carries only the booking time (many schedules). We derive this moment structure from the affine identity of the Hollands-Wald-Zhang and Bonetto-Pound-Sam operators, extend it to second order, where a single quadratic kernel family on rates emerges - - an instantaneous dent and a retarded diagonal θ(2)=κ−1(K∗σ2)\theta^{(2)}=\kappa^{-1}(K*\sigma^2) θ(2)=κ−1(K∗σ2) - - and compute the complete Riemann-squared-sector ledger on a tidally deformed Schwarzschild horizon: Sλ3(v)=4πλ3/G−(λ3/GM)A˙(v)S_{\lambda_3}(v)=4\pi\lambda_3/G-(\lambda_3/GM)\dot{A}(v) Sλ3(v)=4πλ3/G−(λ3/GM)A˙(v), so the higher-derivative clock reads the Einstein heating rate. As a closed advanced-time specialization of the known first-order affine relation (Hollands-Wald-Zhang; Visser-Yan), we obtain AAH(v)=AEH(v)−κ−1A˙EH(v)A_{AH}(v)=A_{EH}(v)-\kappa^{-1}\dot{A}_{EH}(v) AAH(v)=AEH(v)−κ−1A˙EH(v), exact at second order and multipole-blind. Applications: a prescription-robustness statement for the Page time with a sharp eight-derivative boundary, and a classical-geometric test of the interior-independence assumption underlying the firewall argument.
Author: Zander, Fabio
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203568372