Holographic c-Function

TL;DR

This paper introduces a new geometric holographic c-function based on null congruences, applicable to various gravitational solutions, and explores its relation to entanglement entropy.

Contribution

It presents a simple, geometric definition of the holographic c-function and applies it to BPS black solutions and domain walls, linking it to entanglement entropy.

Findings

The proposed c-function is consistent with known holographic c-theorems.

It applies to interpolating AdS solutions in supergravity.

The geometric c-function relates to holographic entanglement entropy.

Abstract

We propose a simple and generic holographic $c$-function that is defined purely from geometry by using the non-affine expansion for null congruences. We examined the proposal for BPS black solutions in $\mathcal{N}=2$ gauged supergravity that interpolate between two different dimensional AdS spacetimes and also for domain wall solutions. Moreover, we commented on the relation of this geometric proposal with the one from the holographic entanglement entropy.