Analytic solutions of the geodesic equation in axially symmetric space-times

TL;DR

This paper provides comprehensive analytic solutions to the geodesic equations in various axially symmetric space-times, expressed through Kleinian sigma functions, enhancing understanding of particle trajectories in these complex geometries.

Contribution

It introduces explicit analytic solutions for geodesic equations in multiple axially symmetric space-times using Kleinian sigma functions, extending previous work.

Findings

Solutions cover Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter, and Plebanski--Demianski space-times.

Analytic solutions are expressed in terms of Kleinian sigma functions.

The work enables precise analysis of particle motion in these geometries.

Abstract

The complete sets of analytic solutions of the geodesic equation in Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general Plebanski--Demianski space--times without acceleration are presented. The solutions are given in terms of the Kleinian sigma functions.