The generalized holographic c-function for regular AdS black holes

• Published in: The European physical journal. C, Particles and fields Vol. 82; no. 6; pp. 1 - 12
• Main Authors: Li, Yang, Miao, Yan-Gang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2022; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Advertising executives; Astronomy; Astrophysics and Cosmology; Asymptotic properties; Behavior; Black holes; Elementary Particles; Entropy; Fixed points (mathematics); Gravity; Hadrons; Heavy Ions; Holography; Horizon; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Spacetime; String Theory
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-022-10458-y

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.