World-Line Perturbation Theory
- 453 Downloads
The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of the strict impossibility to accommodate point masses and rigid bodies. In many situations of practical interest it can still be made to work using an effective hamiltonian or energy-momentum tensor for a finite number of collective degrees of freedom of the compact object. Even so exact solutions of the equations of motion are often not available. In such cases families of world lines of compact bodies in curved space-times can be constructed by a perturbative procedure based on generalized geodesic deviation equations. Examples for simple test masses and for spinning test bodies are presented.
I am indebted to Richard Kerner, Roberto Collistete jr., Gideon Koekoek, Giuseppe d’Ambrosi, S. Satish Kumar and Jorinde van de Vis for pleasant and informative discussions and collaboration on various aspects of the topics discussed. This work is supported by the Foundation for Fundamental Research of Matter (FOM) in the Netherlands.
- 4.S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972)Google Scholar
- 5.E. Hackmann, Geodesic equations and algebro-geometric methods (2015), arXiv:1506.00804v1 [gr–qc]
- 8.J. Ehlers, F.A.E. Pirani, A. Schild, The geometry of free fall and light propagation, in General Relativity: Papers in Honnor of J.L. Synge, ed. by L. O’Raifeartaigh (Oxford University Press, Oxford, 1972)Google Scholar
- 9.C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman and Co., San Francisco, 1970)Google Scholar
- 12.D. Philipp, D. Puetzfeld, C. Lämmerzahl, On the applicability of the geodesic deviation equation in general relativity (2016), arXiv:1604.07173 [gr–qc]