= Kruskal extension of the five-dimensional Schwarzschild-Tangherlini metric
{c}
{title2=$-UV=e^{2r/r_h}(r-r_h)/(r+r_h)$}
The <tortoise coordinate> is $r_*=r+(r_h/2)\log|(r-r_h)/(r+r_h)|$. Set $u=t-r_*$ and $v=t+r_*$, then $U=-e^{-u/r_h}$ and $V=e^{v/r_h}$ in the right exterior. The extended radial metric is $-r_h^2(r+r_h)^2e^{-2r/r_h}dU\,dV/r^2$, regular at $r=r_h$. The horizons are $UV=0$, while $r=0$ gives $UV=1$ and is a spacelike curvature singularity. Compactification by $\arctan U,\arctan V$ displays two exteriors, a future <black hole> and a past <white hole>.
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