entropy [@Ryu:2006bv; @Ryu:2006ef], defining the integrals we need in order to study the black holes that we will consider in the remaining sections. In the appendix \[app AdS\] we review the results for $AdS_{d+2}$, that will be also employed in the section \[section 2 strips\].\
Given a quantum field theory living on the boundary $\mathbb{R}_t \times \mathbb{R}^d$ of an asymptotically $AdS_{d+2}$ space, we take a $d$ dimensional region $A$ strictly included in the constant time slice of the boundary. Let us take a $d$-dimensional surface $\gamma$ embedded in the constant time slice of $AdS_{d+2}$ defined by $z = z(\vec{x})$, being $z$ is the holographic coordinate and $\vec{x} \in \mathbb{R}^d$ a vector of the constant time section of the boundary. The area of $\gamma$ reads $$\textrm{Area}(\gamma) = \int dx_1 \dots dx_d \,\sqrt{\textrm{det}(h_{ij})}$$ where $h_{ij}$ is the induced metric on the surface $ds^2_{\textrm{ind}} =h_{ij} dx^i dx^j$. Among all these surfaces, we restrict our attention to the ones whose boundary coincides with the boundary of the region $A$. Within this smaller subset of surfaces, we denote by $\gamma_A$ the one having minimal area.\
The proposal of Ryu and Takayanagi [@Ryu:2006bv; @Ryu:2006ef] is that we can holographically compute the entanglement entropy in the boundary 