the field equations (\[Geq\]) and (\[BIeq\]) is $$\mathcal{I}_{G}=-\frac{1}{16\pi }\int_{\mathcal{M}}d^{n+1}x\sqrt{-g}%
[R-2\Lambda +\alpha _{2}\mathcal{L}_{2}+\alpha _{3}\mathcal{L}_{3}+\mathcal{L%
}(\mathcal{F})]+\mathcal{I}_{b},  \label{Ibulk}$$where $\mathcal{L}_{2}$, $\mathcal{L}_{3}$ and $\mathcal{L}(\mathcal{F})$were defined before. The last term in Eq. \[Ibulk\] is boundary action. The integral of Eq. \[Ibulk\] does not have a well-defined variational principle, since one encounters a total derivative that produces a surface integral involving the derivative of $\delta g_{\mu \nu }$ normal to the boundary. The normal derivative terms do not vanish by themselves, but are cancelled by the variation of the suitable surface term (Gibbons-Hawking-York boundary term [@GH1; @GH2]) with the following explicit form$$\mathcal{I}_{b}=-\frac{1}{8\pi }\int_{\partial \mathcal{M}}d^{n}x\sqrt{%
-\gamma }\left[ K+\alpha _{2}L_{2b}+\alpha _{3}L_{3b}\right] ,
\label{Iboundary}$$with$$L_{2b}=2\left( J-2\widehat{G}_{ab}^{(1)}K^{ab}\right) ,  \label{L2b}$$$$L_{3b}=3(P-2\widehat{G}_{ab}^{(2)}K^{ab}-12\widehat{R}_{ab}J^{ab}+2\widehat{R%
}J-4K\widehat{R}_{abcd}K^{ac}K^{bd}-8\widehat{R}%
_{abcd}K^{ac}K_{e}^{b}K^{ed}),  \label{L3b}$$where $\gamma _{\mu \nu }$ and $K$ are, respectively, the induced metric and the trace of extrinsic curvature of boundary, $\widehat{G}_{ab}^{(1)}$ and $%
\widehat{G}_{ab}^{(2)}$ denote the $n$-dimensional Einstein and second order Lovelock tensors of the metric $\gamma _{ab}$ while $J$ and $P$ are the traces of $$J_{ab}=\frac{1}{3}%
(2KK_{ac}K_{b}^{c}+K_{cd}K^{cd}K_{ab}-2K_{ac}K^{cd}K_{db}-K^{2}K_{ab}),
\label{Jab}$$and $$\begin{aligned}
P_{ab} &=&\frac{1}{5}%
\{[K^{4}-6K^{2}K^{cd}K_{cd}+8KK_{cd}K_{e}^{d}K^{ec}-6K_{cd}K^{de}K_{ef}K^{fc}+3(K_{cd}K^{cd})^{2}]K_{ab}
\nonumber \\
&&-(4K^{3}-12KK_{ed}K^{ed}+8K_{de}K_{f}^{e}K^{fd})K_{ac}K_{b}^{c}-24KK_{ac}K^{cd}K_{de}K_{b}^{e}
\nonumber \\
&&+12(K^{2}-K_{ef}K^{ef})K_{ac}K^{cd}K_{db}+24K_{ac}K^{cd}K_{de}K^{ef}K_{bf}%
\}.  \label{Pab}\end{aligned}$$

In general the action $\mathcal{I}_{G}$, the Hamiltonian and other associated conserved quantities diverge when evaluated on the solutions. Due to the fact that our spacetime is asymptotically adS, one can 