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| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2026
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| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.5281/zenodo.20126091 |
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Inhaltsangabe:
- <p>We translate four standard results of general relativity — gravitational time dilation, the Tolman temperature law, the Bekenstein–Hawking entropy formula, and Jacobson's (1995) thermodynamic derivation of the Einstein field equations — into the vocabulary of the static gravitational entropy escrow framework [1]. We show that the standard expressions for these results admit a single re-reading: the entropy S_esc held in escrow against the local Unruh temperature by gravitationally bound mass-energy is the same object whose flow appears in Jacobson's first law, whose magnitude equals the Bekenstein–Hawking entropy for a Schwarzschild horizon exactly, and whose product with the local Unruh temperature governs the gravitational redshift via the Tolman relation. The time-dilation leg of this translation is restricted to the weak-field regime; the exact Schwarzschild factor is recovered through the Tolman relation as an exact statement of GR, not through extension of the escrow translation itself. None of the underlying physics is modified by this translation. The framework's contribution at the level treated in this paper is interpretive: it provides a thermodynamic re-reading of these four results, identifying a single thermodynamic ratio — S_esc = |U_grav|/T_U — through which they can be expressed as faces of one identity. We are explicit that this 'single object' is partly notational: |U_grav| takes regime-specific forms across the four translation legs that have not yet been connected by a single covariant construction, and T_U is used with two related but distinct conventions connected by the Tolman shift (§V.G, §V.H). The unification at the level of the algebraic form S = |U|/T is real; the unification at the level of a single covariant observable is partial and remains an open theoretical task. We explicitly do not derive Einstein's equations, the BW asymptote of the modular Hamiltonian, or any new equation of motion. The lattice tests of [2] establish that the modular-Hamiltonian leg of this translation holds partially in 1+1D (approximate recovery of the Bisognano–Wichmann linear asymptote at small distances from the cut, with a 1/30 prefactor suppression whose origin is open), and shows a qualitatively different functional form in 3+1D within the lattice sizes presently accessible (peaked-then-decaying rather than monotonically linear). We discuss what this dimensional dependence means for the translation, and identify the prefactor's origin and the 3+1D rate-of-approach question as the principal open theoretical problems. This is a translation paper, not a derivation paper: its contribution is conceptual re-reading rather than new equations or new predictions. The single calculation that would promote it from interpretive synthesis to constraining theoretical proposal is a first-principles derivation of the 1/30 prefactor from lattice-regulated free QFT; until that calculation succeeds, the framework's identification of the escrow entropy with the modular-Hamiltonian content of a localized perturbation remains a candidate proposal rather than a confirmed identity.</p>