Entanglement Entropy in Horndeski Gravity

TL;DR

This paper investigates how Horndeski gravity influences holographic entanglement entropy in AdS/CFT, revealing the impact of Horndeski parameters on information content and thermodynamic properties of subsystems.

Contribution

It introduces a novel analysis of entanglement entropy in Horndeski gravity, including the effects of parameters on information and thermodynamics in AdS/CFT.

Findings

Horndeski parameters affect entanglement entropy behavior.

Small subsystems obey the first law of entanglement thermodynamics.

Entanglement entropy varies with the parameter  in the model.

Abstract

In this work, we explore the holographic entanglement entropy with an infinite strip region of the boundary in Horndeski gravity. In our prescription we consider the spherically and planar topologies black holes in the AdS$_{4}$/CFT$_{3}$ scenario. In such framework, we show the behavior of the entanglement entropy in function of the Horndeski parameters. Such parameters modify the information store of subsystem A, especially when the parameter $\gamma$ increases the information about the subsystem will also increase or decrease when it decreases. Thus, with this scheme we compute the first law of entanglement thermodynamics in Horndeski gravity and we show that a very small subsystem obeys the analogous property of the first law of thermodynamics if we excite the system.