  In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic)
characterization of a reference spacetime metric $g_0$ consists of a set of
tensorial equations $T[g]=0$, constructed covariantly out of the metric $g$,
its Riemann curvature and their derivatives, that are satisfied if and only if
$g$ is locally isometric to the reference spacetime metric $g_0$. We give the
first IDEAL characterization of generalized Schwarzschild-Tangherlini
spacetimes, which consist of $\Lambda$-vacuum extensions of higher dimensional
spherically symmetric black holes, as well as their versions where spheres are
replaced by flat or hyperbolic spaces. The standard Schwarzschild black hole
has been previously characterized in the work of Ferrando and S\'aez, but using
methods highly specific to $4$ dimensions. Specialized to $4$ dimensions, our
result provides an independent, alternative characterization. We also give a
proof of a version of Birkhoff's theorem that is applicable also on
neighborhoods of horizon and horizon bifurcation points, which is necessary for
our arguments.
