}R_{%
\phantom{\rho \tau}{ \mu \kappa}}^{\rho \tau }+24R^{\mu \nu \sigma \kappa
}R_{\sigma \kappa \nu \rho }R_{\phantom{\rho}{\mu}}^{\rho }  \nonumber \\
&&+3RR^{\mu \nu \sigma \kappa }R_{\sigma \kappa \mu \nu
}-12RR_{\mu \nu }R^{\mu \nu }+24R^{\mu \nu \sigma \kappa
}R_{\sigma \mu }R_{\kappa \nu }+16R^{\mu \nu }R_{\nu \sigma
}R_{\phantom{\sigma}{\mu}}^{\sigma} +R^{3}. \label{L3}\end{aligned}$$In addition, $\alpha _{i}$’s are Lovelock coefficients and $\mathcal{L}_{%
\mathcal{F}}=\frac{d\mathcal{L}(\mathcal{F})}{d\mathcal{F}}$. Now, we consider the following line element to obtain the $(n+1)$-dimensional static topological black hole solutions: $$ds^{2}=-f(r)dt^{2}+\frac{dr^{2}}{f(r)}+r^{2}d\breve{g}^{2}  \label{Metric}$$where $d\breve{g}^{2}$ is the metric of an $(n-1)$-dimensional hypersurface with constant curvature $(n-1)(n-2)k$ and volume $V_{n-1}$ with the following explicit form $$d\breve{g}^{2}=\left\{
\begin{array}{cc}
d\theta _{1}^{2}+\sum\limits_{i=2}^{n-1}\prod\limits_{j=1}^{i-1}\sin
^{2}\theta _{j}d\theta _{i}^{2} & k=1 \\
d\theta _{1}^{2}+\sinh ^{2}\theta _{1}d\theta _{2}^{2}+\sinh ^{2}\theta
_{1}\sum\limits_{i=3}^{n-1}\prod\limits_{j=2}^{i-1}\sin ^{2}\theta
_{j}d\theta _{i}^{2} & k=-1 \\
\sum\limits_{i=1}^{n-1}d\phi _{i}^{2} & k=0%
\end{array}%
\right. .  \label{met2}$$Since the boundary of these spacetimes may be positive, zero or negative constant curvature, these metric is usually called topological spacetime. At first we consider the electromagnetic equation (\[BIeq\]), to obtain the nonzero component of the gauge potential $$A_{\mu }=\delta _{\mu }^{0}\times \left\{
\begin{array}{cc}
-\frac{{\beta r\sqrt{{L}_{W}}}}{{2(n-2)(3n-4)}}\left( {(n-1)\,\zeta {L}%
_{W}+3n-4}\right) , & \text{ENED} \\
\frac{{2{\beta ^{2}}{r^{n}}}}{{nq}}\left( \eta {-1}\right) , & \text{LNED}%
\end{array}%
\right. ,  \label{Amu1}$$where $q$ is an integration constant which is related to the electric charge and $${L}_{W}=LambertW\left( 