The generalized holographic $c$-function for regular AdS black holes

Abstract

We use the entropy density of causal horizons to study the asymptotic behaviors of regular AdS black holes. In some literature, the entropy density of causal horizons is regarded as a generalized holographic c-function. In this paper, we apply this idea to the case of regular AdS black holes. We show that the entropy density decreases to zero at the center of regular AdS black holes and in particular it is stationary because its derivative with respect to the affine parameter approaches zero asymptotically. Therefore, we conclude that the center of regular AdS black holes corresponds to the IR fixed point, which implies that there is no loss of quantum correlation at the center of regular black holes, unlike the case of singular black holes.