Kruskal extension of the five-dimensional Schwarzschild-Tangherlini metric ($-UV=e^{2r/r_h}(r-r_h)/(r+r_h)$)

The tortoise coordinate is $r_{\ast }=r+(r_h/2)\log |(r-r_h)/(r+r_h)|$. Set $u=t-r_{\ast }$ and $v=t+r_{\ast }$, then $U=-e^{-u/r_h}$ and $V=e^{v/r_h}$ in the right exterior. The extended radial metric is $-r_h^2(r+r_h{)}^2{e}^{-2r/r_h}dUdV/r^2$, 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.