Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity

TL;DR

This paper investigates the properties of dynamical black holes with symmetry in higher-dimensional Einstein-Gauss-Bonnet gravity, revealing differences between GR and non-GR branches and deriving entropy laws for trapping horizons.

Contribution

It classifies dynamical black hole solutions in Einstein-Gauss-Bonnet gravity into GR and non-GR branches and analyzes their horizon properties and entropy behavior.

Findings

In the GR branch, trapping horizons behave like those in general relativity.

In the non-GR branch, horizons are non-spacelike with non-increasing area.

The entropy of trapping horizons is non-decreasing in both branches.

Abstract

We explore various aspects of dynamical black holes defined by a future outer trapping horizon in $n(\ge 5)$-dimensional Einstein-Gauss-Bonnet gravity. In the present paper, we assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space and the Gauss-Bonnet coupling constant is non-negative. Depending on the existence or absence of the general relativistic limit, solutions are classified into GR and non-GR branches, respectively. Assuming the null energy condition on matter fields, we show that a future outer trapping horizon in the GR branch possesses the same properties as that in general relativity. In contrast, that in the non-GR branch is shown to be non-spacelike with its area non-increasing into the future. We can recognize this peculiar behavior to arise from a fact that the null energy condition necessarily leads to the null convergence condition for radial null vectors in the GR branch, but not in the non-GR branch. The energy balance law yields the first law of a trapping horizon, from which we can read off the entropy of a trapping horizon reproducing Iyer-Wald's expression. The entropy of a future outer trapping horizon is shown to be non-decreasing in both branches along its generator.