| _version_ | 1866902260755202048 |
|---|---|
| author | Enzo Cabrera Iglesias |
| author_facet | Enzo Cabrera Iglesias |
| contents | <p>This preprint is Sector I (Stationary Black Holes) of the Horizon Response Principle (HRP) triptych (BH / Local Rindler / FLRW). It provides a constants-explicit, sector-typed normalization card for 4D Einstein–Hilbert gravity in the stationary black-hole setting.</p> <p>Scope:<br>• 4D Einstein gravity only<br>• Stationary Killing horizons<br>• Reversible (near-equilibrium) area channel only<br>• All constants explicit (G, c, ħ, k_B)<br>• No new dynamics or modified field equations</p> <p>Sector typing (BH sector).<br>The left-hand side (LHS) object is the Hamiltonian/Noether-charge area contribution in the Iyer–Wald first-law identity, δH_ξ|_area.<br>It is not a matter heat flux δQ and is not identified with LHS objects from other sectors.</p> <p>Normalization backbone.<br>Using the acceleration temperature<br>T(α_H) = ħ α_H / (2π k_B c)<br>and the Einstein (Wald/Bekenstein–Hawking) entropy density<br>S_grav/A = k_B c^3 / (4G ħ),<br>the algebraic identity<br>T(α_H)(S_grav/A) = α_H c^2 / (8πG)<br>exposes a classical coefficient skeleton that HRP packages via</p> <p>k_SEG := 4πG / c^3.</p> <p>In the BH sector the abstract acceleration scale specializes to the physical surface gravity κ, yielding the standard first-law reversible area term in constants-explicit form.</p> <p>Surface-gravity normalization.<br>The paper explicitly distinguishes geometric surface gravity (units 1/m) from physical surface gravity (units m/s^2), related by κ = c^2 κ_geom. All temperature inputs use the physical acceleration scale. This chart pin prevents normalization drift in cross-paper comparisons.</p> <p>What is not claimed.<br>• No derivation or modification of GR<br>• No identification of gravitational entropy with entanglement entropy<br>• No non-equilibrium or entropy-production terms<br>• No universality beyond 4D Einstein gravity<br>• No cross-sector identification of distinct LHS objects</p> <p>Within the HRP suite, this paper establishes the stationary black-hole normalization ledger that anchors the companion Local Rindler and FLRW sector cards. Across sectors, k_SEG functions as a reusable constants-explicit slot, while each sector’s physical LHS object remains strictly typed and non-identified.</p> <p><span>Version note (v2): Suite-wide “Interface Contract” added to enforce typed-LHS discipline, operator-form separation (delta-form vs dot-form), coefficient-only universality, magnitude-first sign policy, and an explicit Entropy Firewall (EF) (S_grav remains Wald/Bekenstein–Hawking gravitational entropy in Einstein gravity; no identification with entanglement/generalized entropy). UHRA “universal” language is now uniformly scoped at first use to mean: within the HRP suite at coefficient level only (4D Einstein gravity under pinned conventions). The BH sector now presents the area channel magnitude-first as the default; a signed form is treated as optional and given only after pinning explicit Iyer–Wald conventions (binormal orientation and Hamiltonian sign convention). Pinned conventions were expanded to clarify stationarity/non-extremality (bifurcate Killing horizon; extremal only as limits), fixed-theory delta-variations with couplings/constants held fixed (including Lambda when present) and horizon-generator normalization held fixed, plus a suite notation crosswalk for the shared slots (k_SEG, T(alpha_H), S_grav/A). Added a bifurcation-surface structural anchor explaining why the horizon contribution reduces to the Noether-charge piece (xi = 0 on B, so xi·Theta vanishes) and included a Schwarzschild sanity check under the pinned sign convention. Core normalization and coefficient skeleton are unchanged: the reversible area coefficient remains (kappa/2c) k_SEG^{-1} = kappa c^2/(8 pi G), and the physical-vs-geometric surface gravity chart pin is retained.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18856678 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Horizon Response Principle (HRP) Sector I: Stationary Black Holes Enzo Cabrera Iglesias Horizon Response Principle HRP kSEG spacetime response constant reversible horizon area response constants-explicit Einstein-Hilbert gravity semantic typing convention locks stationary black holes Iyer-Wald formalism Noether charge first law of black hole mechanics surface gravity (physical) horizon area variation <p>This preprint is Sector I (Stationary Black Holes) of the Horizon Response Principle (HRP) triptych (BH / Local Rindler / FLRW). It provides a constants-explicit, sector-typed normalization card for 4D Einstein–Hilbert gravity in the stationary black-hole setting.</p> <p>Scope:<br>• 4D Einstein gravity only<br>• Stationary Killing horizons<br>• Reversible (near-equilibrium) area channel only<br>• All constants explicit (G, c, ħ, k_B)<br>• No new dynamics or modified field equations</p> <p>Sector typing (BH sector).<br>The left-hand side (LHS) object is the Hamiltonian/Noether-charge area contribution in the Iyer–Wald first-law identity, δH_ξ|_area.<br>It is not a matter heat flux δQ and is not identified with LHS objects from other sectors.</p> <p>Normalization backbone.<br>Using the acceleration temperature<br>T(α_H) = ħ α_H / (2π k_B c)<br>and the Einstein (Wald/Bekenstein–Hawking) entropy density<br>S_grav/A = k_B c^3 / (4G ħ),<br>the algebraic identity<br>T(α_H)(S_grav/A) = α_H c^2 / (8πG)<br>exposes a classical coefficient skeleton that HRP packages via</p> <p>k_SEG := 4πG / c^3.</p> <p>In the BH sector the abstract acceleration scale specializes to the physical surface gravity κ, yielding the standard first-law reversible area term in constants-explicit form.</p> <p>Surface-gravity normalization.<br>The paper explicitly distinguishes geometric surface gravity (units 1/m) from physical surface gravity (units m/s^2), related by κ = c^2 κ_geom. All temperature inputs use the physical acceleration scale. This chart pin prevents normalization drift in cross-paper comparisons.</p> <p>What is not claimed.<br>• No derivation or modification of GR<br>• No identification of gravitational entropy with entanglement entropy<br>• No non-equilibrium or entropy-production terms<br>• No universality beyond 4D Einstein gravity<br>• No cross-sector identification of distinct LHS objects</p> <p>Within the HRP suite, this paper establishes the stationary black-hole normalization ledger that anchors the companion Local Rindler and FLRW sector cards. Across sectors, k_SEG functions as a reusable constants-explicit slot, while each sector’s physical LHS object remains strictly typed and non-identified.</p> <p><span>Version note (v2): Suite-wide “Interface Contract” added to enforce typed-LHS discipline, operator-form separation (delta-form vs dot-form), coefficient-only universality, magnitude-first sign policy, and an explicit Entropy Firewall (EF) (S_grav remains Wald/Bekenstein–Hawking gravitational entropy in Einstein gravity; no identification with entanglement/generalized entropy). UHRA “universal” language is now uniformly scoped at first use to mean: within the HRP suite at coefficient level only (4D Einstein gravity under pinned conventions). The BH sector now presents the area channel magnitude-first as the default; a signed form is treated as optional and given only after pinning explicit Iyer–Wald conventions (binormal orientation and Hamiltonian sign convention). Pinned conventions were expanded to clarify stationarity/non-extremality (bifurcate Killing horizon; extremal only as limits), fixed-theory delta-variations with couplings/constants held fixed (including Lambda when present) and horizon-generator normalization held fixed, plus a suite notation crosswalk for the shared slots (k_SEG, T(alpha_H), S_grav/A). Added a bifurcation-surface structural anchor explaining why the horizon contribution reduces to the Noether-charge piece (xi = 0 on B, so xi·Theta vanishes) and included a Schwarzschild sanity check under the pinned sign convention. Core normalization and coefficient skeleton are unchanged: the reversible area coefficient remains (kappa/2c) k_SEG^{-1} = kappa c^2/(8 pi G), and the physical-vs-geometric surface gravity chart pin is retained.</span></p> |
| title | Horizon Response Principle (HRP) Sector I: Stationary Black Holes |
| topic | Horizon Response Principle HRP kSEG spacetime response constant reversible horizon area response constants-explicit Einstein-Hilbert gravity semantic typing convention locks stationary black holes Iyer-Wald formalism Noether charge first law of black hole mechanics surface gravity (physical) horizon area variation |
| url | https://doi.org/10.5281/zenodo.18856678 |