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- Title
Complex null geodesics in the extended Schwarzschild universe.
- Authors
Holland, Jonathan; Sparling, George
- Abstract
The generic null geodesic of the Schwarzschild-Kruskal-Szekeres geometry has a natural complexification, an elliptic curve with a cusp at the singularity. To realize that complexification as a Riemann surface without a cusp, and also to ensure conservation of energy at the singularity, requires a branched cover of the space-time over the singularity, with the geodesic being doubled as well to obtain a genus two hyperelliptic curve with an extra involution. Furthermore, 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.
- Subjects
GEODESICS; SCHWARZSCHILD black holes; ELLIPTIC curves; HYPERELLIPTIC integrals; CONFORMAL geometry
- Publication
General Relativity & Gravitation, 2018, Vol 50, Issue 7, p1
- ISSN
0001-7701
- Publication type
Article
- DOI
10.1007/s10714-018-2407-z