behavior near the horizon in the $T=0$ case reads [@Herzog:2009gd] $$\label{klebanov bh g}
g(r) \,=\, b (r-r_0)^{13/3} + \dots
\hspace{2cm} b\,\equiv\,\frac{93312\,\sqrt[3]{12}}{25}\;.$$ As checked in the section \[section nh charged bh\] for the charged black hole, the near horizon region determines the leading divergence of the finite term of the holographic entanglement entropy as the strip in the boundary becomes large. Thus, we perform the expansion discussed at the beginning of the section \[section near horizon\] by using the near horizon geometry (\[klebanov bh g\]) instead of the full metric (which is still analytically unknown). Introducing $r_{\textrm{min}} = r_0+ \varepsilon\rho_{\textrm{min}}$ with finite $\rho_{\textrm{min}}$ and changing the integration variable accordingly ($r = r_0+ \varepsilon\rho$), we get for the leading behavior of the integral in (\[L ABansatz\]) the following result $$\label{L warped bh}
\frac{L}{2} \,=\,
\frac{1}{\sqrt{6b \,r_0}\,\varepsilon^{5/3}}\,
\int^{\infty}_{\rho_{\textrm{min}}}\frac{d\rho}{\rho^{13/6}(\rho-\rho_{\textrm{min}})}\,+ \dots
\,=\,
\frac{1}{\sqrt{6b \,r_0}}
\frac{\sqrt{\pi}\,\Gamma\big(\tfrac{5}{3}\big)}{\Gamma\big(\tfrac{13}{6}\big)\,(r_{\textrm{min}}-r_0)^{5/3}}
 +\,\dots$$ where $\dots$ denote higher orders in $\varepsilon$. The same procedure can be applied to the integral in (\[area r finite integ 1\]) which provides the leading divergence of the finite term in the holographic entanglement entropy as $r_{\textrm{min}}$ approaches the horizon. The result reads $$\int_{r_{\textrm{min}}}^{\infty} 
 \Bigg(\,
\frac{r^5}{\sqrt{g(r)}\,\sqrt{r^{6}-r_{\textrm{min}}^{6}}}
-r \Bigg)dr\,=\,
\frac{r_0^{5/2}}{\sqrt{6b}}
\frac{\sqrt{\pi}\,\Gamma\big(\tfrac{5}{3}\big)}{\Gamma\big(\tfrac{13}{6}\big)\,(r_{\textrm{min}} -r_0)^{5/3}}
 +\,\dots
\,=\,  r_0^3 \, L  +\,\dots$$ where 