This is a unique model for which a (*) Lorentz manifold admits the group SO(3), whose orbits are the 2-spheres, as an isometry.
In advanced and retarded coordinates for this model, outgoing and ingoing null rays, respectively, are discontinuous. When represented on an embedding diagram, the spatial geometry of this model is the Flamm paraboloid. Analytically extending this model to cover the full spacetime manifold using Kruskal coordinates results in incoming and outgoing radial photon geodesics being continuous straight lines. This is a unique model for which a (*) Lorentz manifold admits the group SO(3), whose orbits are the 2-spheres, as an isometry. As a consequence of Birkhoff's theorem, every rotationally symmetric solution to the vacuum Einstein equations is equivalent to some subset of this metric, which describes the spacetime around a spherically symmetric mass. For 10 points, name this metric that, in naive coordinates, has a singularity at its German namesake's radius.
In advanced and retarded coordinates for this model, outgoing and ingoing null rays, respectively, are discontinuous.
Schwarzschild metric [or: Schwarzschild model, Schwarzschild geometry; until "rotationally symmetric" is read, accept: spherically symmetric spacetime, spherically symmetric black hole]