Hyperelliptic Functions and Motion in General Relativity

Saskia Grunau and Jutta Kunz
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Saskia Grunau: Institut für Physik, Universität Oldenburg, D-26111 Oldenburg, Germany
Jutta Kunz: Institut für Physik, Universität Oldenburg, D-26111 Oldenburg, Germany

Mathematics, 2022, vol. 10, issue 12, 1-20

Abstract: Analysis of black hole spacetimes requires study of the motion of particles and light in these spacetimes. Here exact solutions of the geodesic equations are the means of choice. Numerous interesting black hole spacetimes have been analyzed in terms of elliptic functions. However, the presence of a cosmological constant, higher dimensions or alternative gravity theories often necessitate an analysis in terms of hyperelliptic functions. Here we review the method and current status for solving the geodesic equations for the general hyperelliptic case, illustrating it with a set of examples of genus g = 2 : higher dimensional Schwarzschild black holes, rotating dyonic U ( 1 ) 2 black holes, and black rings.

Keywords: hyperelliptic functions; geodesic motion; black holes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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