= Schwarzschild-Tangherlini metric
{c}
{title2=$f(r)=1-\mu/r^{D-3}$}
= Schwarzschild-Tangherlini black hole
{c}
{synonym}
For $D\geq4$, the static spherical vacuum metric $ds^2=-fdt^2+f^{-1}dr^2+r^2d\Omega_{D-2}^2$ 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.
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