Excess inner-horizon entropy and the thermodynamics of Kerr formation
Abstract
\noindent We develop a charge-matched thermodynamic framework for the regular rotating black-hole family underlying an exact model of Kerr formation. Since the Kerr endpoint already possesses a Cauchy horizon, hidden entropy is identified with the excess inner-horizon area relative to Kerr at fixed mass M and angular momentum J=Ma: Sexc=π[hc2−(r-Kerr)2], where hc is the regular inner-horizon radius and r-Kerr=M−√(M2−a2). Under regularity and interior-profile assumptions, we prove r-Kerr<hc<h and establish the sharp bound 0<Sexc<4πM√(M2−a2). The Schwarzschild limit yields Sexc=πhc2, while Sexc=0 at the Kerr endpoint. The Kerr reference entropy satisfies S+Kerr+S-Kerr=4πM2, so rotation redistributes its two-horizon contributions at fixed mass. For the time-dependent model, we derive exact evolution equations for the inner root and Sexc, interpreted as root-bookkeeping identities unless the roots are established as dynamical horizons. In the minimal N=1 trajectory, the apparent pole at n=2 is removable in the mass profile, giving a logarithmic continuation of the root equation, although the stationary curvature is singular there. The stationary Ricci-scalar density is locally absolutely integrable for −1<n≤2, with the Kerr endpoint n=−1 treated separately. Minkowski breaking occurs at n=0, independently of inner-horizon disappearance. Quasi-extremal regular configurations approach, but cannot attain, the entropy bound without losing a regular Killing horizon.
Related
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BibTeX
@misc{lobo2026excess,
title = {{Excess inner-horizon entropy and the thermodynamics of Kerr formation}},
author = {Francisco S. N. Lobo and Jorge Ovalle and Manuel E. Rodrigues},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00863},
eprint = {2611.00863},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00863},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Excess inner-horizon entropy and the thermodynamics of Kerr formation
AU - Francisco S. N. Lobo
AU - Jorge Ovalle
AU - Manuel E. Rodrigues
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00863
UR - https://arxiv.org/abs/2611.00863
AB - \noindent We develop a charge-matched thermodynamic framework for the regular rotating black-hole family underlying an exact model of Kerr formation. Since the Kerr endpoint already possesses a Cauchy horizon, hidden entropy is identified with the excess inner-horizon area relative to Kerr at fixed mass M and angular momentum J=Ma: Sexc=π[h_c^2−(r_-^Kerr)^2], where h_c is the regular inner-horizon radius and r_-^Kerr=M−√(M^2−a^2). Under regularity and interior-profile assumptions, we prove r_-^Kerr<h_c<h and establish the sharp bound 0<Sexc<4πM√(M^2−a^2). The Schwarzschild limit yields Sexc=πh_c^2, while Sexc=0 at the Kerr endpoint. The Kerr reference entropy satisfies S_+^Kerr+S_-^Kerr=4πM^2, so rotation redistributes its two-horizon contributions at fixed mass. For the time-dependent model, we derive exact evolution equations for the inner root and Sexc, interpreted as root-bookkeeping identities unless the roots are established as dynamical horizons. In the minimal N=1 trajectory, the apparent pole at n=2 is removable in the mass profile, giving a logarithmic continuation of the root equation, although the stationary curvature is singular there. The stationary Ricci-scalar density is locally absolutely integrable for −1<n≤2, with the Kerr endpoint n=−1 treated separately. Minkowski breaking occurs at n=0, independently of inner-horizon disappearance. Quasi-extremal regular configurations approach, but cannot attain, the entropy bound without losing a regular Killing horizon.
ER -