The problem of motion of extended bodies in General Relativity is notorious for its analytical difficulty, but at the same time highly relevant for comparison of theoretical predictions with modern precision measurements in relativistic astrophysics and cosmology. Its one of the most important topics in General Relativity and its application to astrophysics.
We focus attention on two aspects of equations of motion in general relativity: the motion of extended bodies (stars) and the motion of small black holes. Our objective is to offer a guide to prospective researchers into these areas of general relativity and to point out open questions and topics that are ripe for further development. It is over forty years since a text on this subject was published and in that time the research area of equations of motion in general relativity has undergone
extraordinary development, stimulated by the discovery of the binary neutron star PSR 1913+16 in 1974 (which was the first isolated gravitating system found in which general relativity plays a fundamental role in describing theoretically its evolution), and more recently by the advent of kilometre size
interferometric gravitational wave detectors which are expected to detect gravitational waves produced by coalescing binary neutron stars.
Hideki Asada [Research Fellow, previously: Yukawa Institute for Theoretical Physics, Kyoto University; Institut d'Astrophysique de Paris] Toshifumi Futamase [Research Fellow, previously: Max Planck Institute, Munich; Washington University, St. Louis; University College Cardiff] Peter Hogan [Research Fellow, previously: School of Theoretical Physics, Dublin Institute for Advanced Studies; University of Texas, Austin; Trinity College, Dublin]
1. Introduction ; 2. Foundations of the Post Newtonian Approximation ; 3. The Third Post Newtonian Approximation ; 4. Two-Body Problem in General Relativity ; 5. Small Black Holes: Geometrical Preliminaries ; 6. Small Charged Black Holes: Equations of Motion ; 7. Gravitational Physics of Few Body Systems