Complex null geodesics in the extended Schwarzschild universe

The generic null geodesic of the Schwarzschild–Kruskal–Szekeres geometry has a natural complexification, an elliptic curve with a cusp at the singularity

The generic null geodesic of the Schwarzschild–Kruskal–Szekeres geometry has a natural complexification, an elliptic curve with a cusp at the singularity

The resulting space-time obtained from this branch cover has a Hamiltonian that is null geodesically complete

The full complex null geodesic can be realized in a natural complexification of the Kruskal–Szekeres metric

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