**Holographic entanglement entropy:**

**near horizon geometry and disconnected regions**

Erik Tonni

[*Center for Theoretical Physics,*]{}

[*Massachusetts Institute of Technology,*]{}

[*Cambridge, MA 02139, USA*]{}

[tonni@mit.edu]{}

**Abstract**

We study the finite term of the holographic entanglement entropy for the charged black hole in $AdS_{d+2}$ and other examples of black holes when the spatial region in the boundary theory is given by one or two parallel strips. For one large strip it scales like the width of the strip. The divergent term of its expansion as the turning point of the minimal surface approaches the horizon is determined by the near horizon geometry. Examples involving a Lifshitz scaling are also considered. For two equal strips in the boundary we study the transition of the mutual information given by the holographic prescription. In the case of the charged black hole, when the width of the strips becomes large this transition provides a characteristic finite distance depending on the temperature.

Introduction {#introduction .unnumbered}
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Entanglement entropy is an important quantity which has been studied in many models of condensed matter systems, quantum information and quantum gravity. It measures the quantum correlations in a bipartite decomposition of a quantum system.\
Let us consider a system whose 