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

TL;DR

This paper investigates the causal horizon entropy as a generalized holographic c-function in regular AdS black holes, demonstrating its monotonic decrease and stationarity at the center, consistent with IR fixed point behavior.

Contribution

It applies the causal horizon entropy concept to regular AdS black holes, establishing it as a valid holographic c-function candidate with specific asymptotic properties.

Findings

Causal horizon entropy decreases to zero at the black hole center.

Entropy is stationary at the center, indicating an IR fixed point.

Supports causal horizon entropy as a holographic c-function for regular AdS black holes.

Abstract

We use the causal horizon entropy to study the asymptotic behaviors of regular AdS black holes. In some literature, the causal horizon entropy 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 causal horizon entropy 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. Meanwhile, the asymptotic behavior of the metric of regular AdS black holes implies that the black hole center corresponds to an IR fixed point. Therefore, we conclude that the causal horizon entropy is a valid candidate for the holographic $c$-function of these regular AdS black holes.