Im trying to confirm that the metric (11) in the paper below is a solution to Einstein's equations (6). I tried to use the metric and extract $\lambda=(1-(r_+/r)^{D-3})^{1/2-\gamma/2(D-3)}$ and $R=r(1-(r_{-})/r)^{D-3})^\gamma$, but I dont know how to proceed, in addition I dont know how to evaluate the third term in the ricci tensor (6).
the paper:
