Area evolution, bulk viscosity and entropy principles for dynamical horizons

TL;DR

This paper derives an evolution law for dynamical horizons from Einstein's equations, revealing causal behavior and positive bulk viscosity, and proposes an entropy-based principle to select unique horizons in spacetime evolution.

Contribution

It introduces a local, causal evolution law for dynamical horizons with positive bulk viscosity, contrasting with non-causal event horizons, and proposes an entropy principle for horizon selection.

Findings

Derivation of a causal area evolution law from Einstein's equations.

Identification of positive bulk viscosity in the horizon analogy.

Proposal of an entropy-based criterion for horizon selection.

Abstract

We derive from Einstein equation an evolution law for the area of a trapping or dynamical horizon. The solutions to this differential equation show a causal behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted as an energy balance law, yielding to a positive bulk viscosity. These two features contrast with the event horizon case, where the non-causal evolution of the area and the negative bulk viscosity require teleological boundary conditions. This reflects the local character of trapping horizons as opposed to event horizons. Interpreting the area as the entropy, we propose to use an area/entropy evolution principle to select a unique dynamical horizon and time slicing in the Cauchy evolution of an initial marginally trapped surface.