Stability of asymptotically de Sitter and anti-de Sitter black holes in 4D regularized Einstein-Gauss-Bonnet theory

A regularized four-dimensional Einstein-Gauss-Bonnet model has been recently proposed in Glavan and Lin (2020). It was claimed that the approach bypasses the Lovelock theorem. In this approach the four-dimensional solution is constructed through dimensional regularization by taking the limit D -> 4. The consistent formulation of the corresponding four-dimensional theory with broken diffeomorphism invariance was later proposed by Aoki et al. (2020). The consistent theory allows for the same black-hole configurations, which can be obtained via the first regularization approach. Therefore, we find explicitly the parametric regions of stability of the four-dimensional Einstein-Gauss-Bonnet black holes for the asymptotically flat and (anti-)de Sitter spacetimes by analyzing the time-domain profiles for gravitational perturbations in both vector and scalar channels. In addition to the known eikonal instability we find the instability due to the positive cosmological constant. On the contrary, asymptotically anti-de Sitter black holes have no other instability than the eikonal one. (C) 2021 Elsevier B.V. All rights reserved.