Horizon Entropy

TL;DR

The paper argues that horizon thermodynamics extends beyond black holes to all causal horizons by introducing a local horizon entropy density and a universal set of laws. It shows that the generalized second law and first-law relations apply to Killing, de Sitter, and Rindler horizons, and that the Einstein equation can emerge as an equation of state from local horizon thermodynamics, with $S_{BH}=A/4$ and $T_H= obreak\kappa/(2\pi)$. It develops a statistical-mechanical framework for horizon entropy, including back-reaction and area-change based transition rates ${\bf R}=\exp((A_{j'}-A_j)/4)$, and surveys multiple state-counting approaches (Carlip, LQG, strings) while emphasizing that horizon entropy is an observer-dependent, partly holographic notion. The work highlights that, although horizon entropy appears universal across Killing horizons, the precise microscopic origin—potentially tied to quantum shear modes or entanglement—remains an open, active area of research with significant implications for quantum gravity.

Abstract

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, extend quite generally to what we call here "causal horizons". The root of this generalization is the local notion of horizon entropy density.

Figures (1)

• Figure 1: Carter-Penrose diagrams of causal horizons in (conformal compactifications of) various spherically symmetric spacetimes. Each generic point in one of the diagrams represents a 2-sphere of symmetry, and the radial null lines make 45 degree angles with the vertical. The points on the left hand edge of each diagram lie at the origin of spherical symmetry, hence they represent just a single point. The points on the right hand edge of the de Sitter diagram lie at the antipode of the 3-sphere, hence they also represent a single point. Future null infinity is denoted by ${\cal I}^+$ .