Horizon Response Principle (HRP) Sector I: Stationary Black Holes

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. Scope: • 4D Einstein gravity only• Stationary Killing horizons• Reversible (near-equilibrium) area channel only• All constants explicit (G, c, ħ, kB) • No new dynamics or modified field equations Sector typing (BH sector). The left-hand side (LHS) object is the Hamiltonian/Noether-charge area contribution in the Iyer–Wald first-law identity, δH_ξ|ₐrea. It is not a matter heat flux δQ and is not identified with LHS objects from other sectors. Normalization backbone. Using the acceleration temperatureT (αH) = ħ αH / (2π kB c) and the Einstein (Wald/Bekenstein–Hawking) entropy densitySgrav/A = kB c³ / (4G ħ), the algebraic identityT (αH) (Sgrav/A) = αH c² / (8πG) exposes a classical coefficient skeleton that HRP packages via kSEG: = 4πG / c³. 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. Surface-gravity normalization. The paper explicitly distinguishes geometric surface gravity (units 1/m) from physical surface gravity (units m/s²), related by κ = c² κgeom. All temperature inputs use the physical acceleration scale. This chart pin prevents normalization drift in cross-paper comparisons. What is not claimed. • No derivation or modification of GR• No identification of gravitational entropy with entanglement entropy• No non-equilibrium or entropy-production terms• No universality beyond 4D Einstein gravity• No cross-sector identification of distinct LHS objects 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, kSEG functions as a reusable constants-explicit slot, while each sector’s physical LHS object remains strictly typed and non-identified.