Horizon Response Principle (HRP) Sector II: Local Rindler Horizons

This preprint is Sector II (Local Rindler Horizons) 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 local-horizon (Jacobson) setting. Scope:• 4D Einstein gravity only• Local causal (Rindler) horizons in the Jacobson construction• Reversible (near-equilibrium) area channel only• All constants explicit (G, c, ħ, k_B)• No new dynamics or modified field equations Sector typing (Local Rindler sector).The left-hand side (LHS) object is the boost-energy flux integral (Clausius heat) across a local horizon patch, δQ_boost.It is not a BH Hamiltonian/Noether variation and is not identified with LHS objects from other sectors. Normalization backbone.Using the acceleration temperatureT(α_H) = ħ α_H / (2π k_B c)and the Einstein (Wald/Bekenstein–Hawking) entropy densityS_grav/A = k_B c^3 / (4G ħ),the algebraic identityT(α_H)(S_grav/A) = α_H c^2 / (8πG)exposes a classical coefficient skeleton that HRP packages via k_SEG := 4πG / c^3. In the Local Rindler sector the abstract acceleration scale specializes to the physical proper acceleration α (of the accelerated observers at the chosen point), yielding the standard reversible Clausius area-response channel in constants-explicit form within the local-horizon construction. Acceleration normalization.The paper distinguishes the geometric scale κ_geom (units 1/m in a length chart X^0 = ct) from the physical proper acceleration α (units m/s^2), related by α = c^2 κ_geom. All temperature inputs use the physical acceleration scale. This chart pin prevents normalization drift in cross-paper comparisons. Reversible regime (Jacobson pin).The analysis is restricted to a local horizon patch at a spacetime point p with vanishing expansion and shear (θ(p) = 0 = σ_ab(p)). The Clausius relation δQ_boost = T δS_grav is treated as a near-equilibrium constitutive input in this regime. The standard Raychaudhuri bridge is recorded only as a compatibility check with the Einstein equation under these pinned assumptions. What is not claimed.• No claim that thermodynamics independently derives GR beyond the standard Jacobson assumptions• 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 local-horizon normalization ledger that complements the stationary black-hole 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.