TY - JOUR

T1 - Inversion of hyperelliptic integrals of arbitrary genus with application to particle motion in general relativity

AU - Enolski, V.Z.

AU - Hackmann, E.

AU - Lämmerzahl, C.

AU - Kagramanova, V.

AU - Kunz, J.

PY - 2011/5/1

Y1 - 2011/5/1

N2 - 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 a holomorphic hyperelliptic integral. The result of the inversion is defined only locally, and is done 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 sigma 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 theta-constants. The cases of genus 2 and genus 3 are considered in detail. The method is exemplified by particle motion associated with a genus 3 hyperelliptic curve.

AB - 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 a holomorphic hyperelliptic integral. The result of the inversion is defined only locally, and is done 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 sigma 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 theta-constants. The cases of genus 2 and genus 3 are considered in detail. The method is exemplified by particle motion associated with a genus 3 hyperelliptic curve.

UR - http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-79751527244&md5=e9606f37b3608ce1da10806dc845c890

U2 - 10.1016/j.geomphys.2011.01.001

DO - 10.1016/j.geomphys.2011.01.001

M3 - Article

AN - SCOPUS:79751527244

VL - 61

SP - 899

EP - 921

JO - Journal of geometry and physics

JF - Journal of geometry and physics

SN - 0393-0440

IS - 5

ER -