Breakdown of the Equal Area Law for Holographic Entanglement Entropy

TL;DR

This paper examines proposed equal area laws in holographic entanglement entropy and correlation functions for charged AdS black holes, demonstrating numerically that these laws do not hold, challenging recent claims.

Contribution

The paper provides a numerical analysis showing the invalidity of proposed equal area laws in holographic settings, clarifying misconceptions in the field.

Findings

Neither the entanglement entropy nor the correlation function equal area laws hold.

Numerical evidence contradicts recent claims of these laws' validity.

There is no physical basis for such equal area constructions in these holographic planes.

Abstract

We investigate a holographic version of Maxwell's equal area law analogous to that for the phase transition in the black hole temperature/black hole entropy plane of a charged AdS black hole. We consider proposed area laws for both the black hole temperature/holographic entanglement entropy plane and the black hole temperature/2-point correlation function plane. Despite recent claims to the contrary, we demonstrate numerically that neither proposal is valid. We argue that there is no physical reason to expect such a construction in these planes.