Gravitational Thermodynamicization of Primordial Black Holes: An RVB Residue Formulation of Thermal Formation and Nonequilibrium Evolution
Abstract
We establish a controlled, local, and quasi-stationary thermodynamic framework for neutral, nonrotating primordial black holes (PBHs) by combining a local residue prescription with the thermodynamicization of gravitational dynamics. For a nonextremal spherical horizon, we demonstrate that the positive residue of a meromorphic one-form directly determines the inverse Hawking temperature. Applying the first law of thermodynamics recovers the standard Schwarzschild temperature and Bekenstein-Hawking entropy under standard normalization. The resulting entropy defines an off-shell canonical exponent, which reveals that equilibrium thermal production of PBHs is exponentially suppressed in a radiation-dominated universe, thereby confirming that the standard density-perturbation collapse criterion remains the primary formation mechanism. For post-formation evolution, we adopt a detailed-balance mass law, prove the validity of the generalized second law of thermodynamics, and express the evolution dynamics as a free-energy gradient flow where the moving mass acts as an instantaneous evaporation-accretion threshold. Finally, we derive explicit first-order shifts for the temperature, entropy, thermal saddle, and nucleation exponent under small analytic deformations of the residue.
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BibTeX
@misc{chen2026gravitational,
title = {{Gravitational Thermodynamicization of Primordial Black Holes: An RVB Residue Formulation of Thermal Formation and Nonequilibrium Evolution}},
author = {Wen-Xiang Chen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07747},
eprint = {2611.07747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07747},
}
RIS
TY - UNPB
TI - Gravitational Thermodynamicization of Primordial Black Holes: An RVB Residue Formulation of Thermal Formation and Nonequilibrium Evolution
AU - Wen-Xiang Chen
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07747
UR - https://arxiv.org/abs/2611.07747
AB - We establish a controlled, local, and quasi-stationary thermodynamic framework for neutral, nonrotating primordial black holes (PBHs) by combining a local residue prescription with the thermodynamicization of gravitational dynamics. For a nonextremal spherical horizon, we demonstrate that the positive residue of a meromorphic one-form directly determines the inverse Hawking temperature. Applying the first law of thermodynamics recovers the standard Schwarzschild temperature and Bekenstein-Hawking entropy under standard normalization. The resulting entropy defines an off-shell canonical exponent, which reveals that equilibrium thermal production of PBHs is exponentially suppressed in a radiation-dominated universe, thereby confirming that the standard density-perturbation collapse criterion remains the primary formation mechanism. For post-formation evolution, we adopt a detailed-balance mass law, prove the validity of the generalized second law of thermodynamics, and express the evolution dynamics as a free-energy gradient flow where the moving mass acts as an instantaneous evaporation-accretion threshold. Finally, we derive explicit first-order shifts for the temperature, entropy, thermal saddle, and nucleation exponent under small analytic deformations of the residue.
ER -