2011/06/13 by V. Z. Enolski, Victor Enolski, Enolski, Victor +11 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1106.2408
34 pages, 3 figures, 1 table; We extended the sections 'Introduction' and 'Conclusions and Outlook' and made some cosmetic changes throughout the article. The article is accepted for publication in JMP. arXiv admin note: text overlap with arXiv:1011.6459
openalex publication_date 2011/06/13 · arxiv created 2011/12/21 · arxiv updated 2011/12/22 · openalex created_date 2022/09/11 · openalex updated_date 2026/07/28
The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of hyperelliptic integrals of all three kinds. The result of the inversion is defined locally, using the algebro-geometric techniques of the standard Jacobi inversion problem and the foregoing restriction to the θ-divisor. For a representation of the hyperelliptic functions the Klein--Weierstraß multivariable σ-function is introduced. It is shown that all parameters needed for the calculations like period matrices and abelian images of branch points can be expressed in terms of the periods of holomorphic differentials and θ-constants. The cases of genus two, three and four are considered in detail. The method is exemplified by the particle motion associated with genus one elliptic and genus three hyperelliptic curves. Applications are for instance solutions to the geodesic equations in the space-times of static, spherically symmetric Hořava-Lifshitz black holes.