Mechanical laws of the Rindler horizon

TL;DR

This paper explores how gravitational perturbations affect the Rindler horizon, deriving mechanical laws analogous to black hole physics, and discusses implications for quantum gravity and thermodynamics.

Contribution

It introduces a perturbative field-theoretical approach to describe dynamical Rindler horizons and links horizon area changes to matter energy crossing, extending classical laws towards thermodynamics.

Findings

Horizon area change relates to matter energy flux.

Perturbative methods validate horizon dynamics analogies.

Discussion on entanglement entropy and quantum gravity implications.

Abstract

Gravitational perturbations of flat Minkowski space make the Rindler horizon dynamical: the horizon satisfies mechanical laws analogous to the ones followed by black holes. We describe the gravitational perturbation of Minkowski space using perturbative field-theoretical methods. The change in the area of the Rindler horizon is described in terms of the deflection of light rays by the gravitational field. The difference between the area of the perturbed and the unperturbed horizon is related to the energy of matter crossing the horizon. We derive consistency conditions for the validity of our approximations, and compare our results to similar ones present in the literature. Finally, we discuss how this setting can be used in perturbative quantum gravity to extend the classical mechanical laws to thermodynamic laws, with the entanglement of field modes across the Rindler horizon providing a notion of thermodynamic entropy.