Integrals of Motion in Curved Space-Time

Abstract

Integrals of motion are the quantities that remain constant during the motion of a point particle that allow to determine various important properties without solving the equations of motion. In this thesis, a systematic analysis for the motion of a relativistic particle in curved space-time is given and the relation of the integrals of motion to the Killing vectors and the Killing tensors of the space-time in which the particle moves is explained. As examples, motion on the Schwarzschild, the Kerr and the generalized Lense-Thirring space-times are studied.