a function of $L$ (red line). For small $L$ it recovers the corresponding quantity for $AdS_4$ (blue curve) obtained from (\[Atilde free\]). The black line provides the large $L$ behavior given by (\[expansion nh rn T0\]). \[finite area L\]](AreafiniteLT0 "fig:"){width="7.5cm"}      ![Extremal charged black hole in $AdS_4$ with $z_0=1$ (left) and $z_0=1.5$ (right). Plot of the finite term $\mathcal{A}_2(z_{\textrm{max}},0)$ as a function of $L$ (red line). For small $L$ it recovers the corresponding quantity for $AdS_4$ (blue curve) obtained from (\[Atilde free\]). The black line provides the large $L$ behavior given by (\[expansion nh rn T0\]). \[finite area L\]](AreafiniteLT0plot2 "fig:"){width="7.5cm"}
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$\bullet$ [**Non extremal charged black hole.**]{} The same method applied for $T>0$ leads to $$\label{L exp extremal ddim}
L\,=\,
-\,\frac{\sqrt{z_0}}{\sqrt{2\pi d\, T}}\,\log(z_0-z_{\textrm{max}})
+ O(1)$$ and $$\label{expansion nh rn T}
\mathcal{A}_d(z_{\textrm{max}},0)
\,=\,
-\,\frac{\sqrt{z_0}}{z_0^d\sqrt{2\pi d\, T}}\,\log(z_0-z_{\textrm{max}})
+ O(1)
\,=\,\frac{L}{z_0^{d}}
+ O(1)\;.$$ Comparing these three regimes of the same black hole, one learns that the finite term of the holographic entanglement entropy diverges like the width $L$ (and therefore like the volume) of the strip in the boundary. The distinguished feature is the kind of divergence of $\mathcal{A}_d(z_{\textrm{max}},0)$ and $L$ as $z_{\textrm{max}} \rightarrow z_0$. This is determined by the near horizon 