Fabiano Francisco dos Santos - Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil.

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_{۴}/CFT_{۳} 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.

Holographic Entanglement, Horndeski Gravity, Field Theory