}{r^{2n-2}}  \label{flarge} \\
&&-\frac{4\alpha mq^{2}}{(n-1)(n-2)r^{3n-4}}+\frac{4\alpha q^{4}}{%
(n-1)^{2}(n-2)^{2}r^{4n-6}}-\frac{4\left[ n(n-1)-4\alpha \Lambda \right]
q^{4}}{\Upsilon n(3n-4)\beta ^{2}r^{4n-6}}+O(\frac{1}{r^{5n-6}}),  \nonumber
\\
&&  \nonumber \\
\Upsilon &=&\left\{
\begin{array}{cc}
2(n-1)^{2} & ENED \\
n^{2} & LNED%
\end{array}%
\right. .  \nonumber\end{aligned}$$Eq. (\[flarge\]) shows that the second term is dominant for large $r$ in which confirms that these black holes are asymptotically adS if we replace $%
\Lambda $ with $\Lambda _{eff}=\frac{\Lambda \left[ n(n-1)-2\alpha \Lambda %
\right] }{n(n-1)}$. In other words, Lovelock gravity may modify the cosmological constant and, as we expect, $\Lambda _{eff}\longrightarrow
\Lambda $ for vanishing $\alpha $.

$%
\begin{array}{cc}
\epsfxsize=5.3cm \epsffile{penrose1b.eps} & \epsfxsize=8cm %
\epsffile{penrose11b.eps}%
\end{array}
$

$%
\begin{array}{cc}
\epsfxsize=4.3cm \epsffile{penrose2b.eps} & \epsfxsize=5.5cm %
\epsffile{penrose22b.eps}%
\end{array}
$

$%
\begin{array}{cc}
\epsfxsize=5.5cm \epsffile{penrose3b.eps} & \epsfxsize=8.5cm %
\epsffile{penrose33b.eps}%
\end{array}
$

In order to provide additional information for the conformal structure of the solutions, we can use the conformal compactification method to draw the Carter-Penrose (conformal) diagram (see Figs. \[Pen1\]-\[Pen3\] for more details). The Carter-Penrose diagrams confirm that the singularity may be timelike (such as Reissner-Nordström black holes) or spacelike (such as Schwarzschild black holes). In other words, depending the values of the nonlinearity parameter, one can find that $\lim_{r
\longrightarrow 0}f(r)$ can be positive or negative (for more details we 