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

We explore various aspects of dynamical black holes defined by a future outer trapping horizon in n(≥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 that this peculiar behavior arises from the 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