What question did this study set out to answer?

The aim is to provide a normalization framework for local Rindler horizons within the context of 4D Einstein gravity.

March 1, 2026Open Access

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

Key Points

The aim is to provide a normalization framework for local Rindler horizons within the context of 4D Einstein gravity.
Derive a constants-explicit normalization for the local Rindler sector.
Utilize the Clausius relation for energy flux at local horizons.
Differentiate between geometric scale and proper acceleration in a near-equilibrium context.
Establishes a classical coefficient skeleton through an algebraic identity involving acceleration and entropy density.
Confirms that the Clausius area-response channel operates within a local-horizon setting.
Clarifies restrictions on the applicability of thermodynamic principles in this context.

Abstract

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, kB) • 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, δQboost. It is not a BH Hamiltonian/Noether variation 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 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 κgeom (units 1/m in a length chart X⁰ = ct) from the physical proper acceleration α (units m/s²), related by α = c² κgeom. 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 = σₐb (p) ). The Clausius relation δQboost = T δSgrav 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, kSEG functions as a reusable constants-explicit slot, while each sector’s physical LHS object remains strictly typed and non-identified.

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

Key Points

Abstract

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