 Schwarzschild-Tangherlini metric

For $D\ge 4$, the static spherical vacuum metric $d{s}^2=-fd{t}^2+f^{-1}d{r}^2+r^{2}d{\Omega }_{D-2}^2$ has an event horizon at $r_h={\mu }^{1/(D-3)}$. With time normalized at infinity its ADM mass is $M=(D-2){\Omega }_{D-2}\mu /(16\pi G_D)$, where ${\Omega }_{D-2}$ is the unit-sphere area. For $D=5$ and $\mu =2m$, $r_h=\sqrt{2m}$ and $M=3\pi m/(4G_5)$. The spherical orbits are three-spheres, even though the radial-time Penrose diagram has the same causal pattern as its four-dimensional counterpart.