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Hyperelliptic functions and geodesic equations
Author(s) -
Hackmann Eva,
Lämmerzahl Claus
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810723
Subject(s) - geodesic , mathematics , pure mathematics , schwarzschild radius , riemann surface , riemann hypothesis , genus , hyperelliptic curve , divisor (algebraic geometry) , mathematical physics , mathematical analysis , algebra over a field , physics , spacetime , quantum mechanics , botany , biology
A method for solving geodesic equations in Schwarzschild–de Sitter space–times and higher dimensional Schwarzschild space–times is presented. The solutions are derived from Jacobi's inversion problem on a Riemann surface of genus 2 restricted to the set of zeros of the theta function, which is called a theta–divisor. In its final form, the solutions are given in terms of derivatives of Kleinian sigma functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)