How Much Geometry Does Horizon Entropy Determine? A Discourse on Entropy, Gravity, and Observable Quantities
Abstract
Building on Jacobson's thermodynamics derivation of Einstein field equations, the "generalized entropy and varying-G" (GEVAG) framework was proposed to consistently incorporate generalized horizon entropy S=f(A)/4G into both the thermodynamics and the geometry of spacetime. This leads to an effective gravitational coupling Geff=G/f'(A). A related "entropy-gravity correspondence" (EGC) instead is equivalent to promoting this horizon relation to a radially varying bulk coupling Geff(r). We clarify the similarities and fundamental distinctions between these approaches. Although they share the same horizon consistency relation, their global causal structures and asymptotic geometries can differ substantially. In addition, the radial prescription of EGC introduces an additional ambiguity for multi-center configurations. We further examine a near-horizon extension of GEVAG, which restores the equivalence between thermodynamic and ADM masses that is absent in the horizon-only formulation. We then discuss the implications of these different prescriptions for the Bekenstein bound. The Bekenstein bound provides a surprising link between Geff in near horizon GEVAG, EGC, and the one obtained in the recent f(R)-reconstruction approach of generalized entropy geometry via Wald entropy. Finally, we raise the most important question: what exactly is the G measured in laboratories?
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BibTeX
@misc{ong2026much,
title = {{How Much Geometry Does Horizon Entropy Determine? A Discourse on Entropy, Gravity, and Observable Quantities}},
author = {Yen Chin Ong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01720},
eprint = {2609.01720},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01720},
}
RIS
TY - UNPB
TI - How Much Geometry Does Horizon Entropy Determine? A Discourse on Entropy, Gravity, and Observable Quantities
AU - Yen Chin Ong
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01720
UR - https://arxiv.org/abs/2609.01720
AB - Building on Jacobson's thermodynamics derivation of Einstein field equations, the "generalized entropy and varying-G" (GEVAG) framework was proposed to consistently incorporate generalized horizon entropy S=f(A)/4G into both the thermodynamics and the geometry of spacetime. This leads to an effective gravitational coupling G_eff=G/f'(A). A related "entropy-gravity correspondence" (EGC) instead is equivalent to promoting this horizon relation to a radially varying bulk coupling G_eff(r). We clarify the similarities and fundamental distinctions between these approaches. Although they share the same horizon consistency relation, their global causal structures and asymptotic geometries can differ substantially. In addition, the radial prescription of EGC introduces an additional ambiguity for multi-center configurations. We further examine a near-horizon extension of GEVAG, which restores the equivalence between thermodynamic and ADM masses that is absent in the horizon-only formulation. We then discuss the implications of these different prescriptions for the Bekenstein bound. The Bekenstein bound provides a surprising link between G_eff in near horizon GEVAG, EGC, and the one obtained in the recent f(R)-reconstruction approach of generalized entropy geometry via Wald entropy. Finally, we raise the most important question: what exactly is the G measured in laboratories?
ER -