Equations of Motion in Relativistic Gravity

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Dirk Puetzfeld, Claus Lämmerzahl, Bernard Schutz
Springer, Jun 1, 2015 - Science - 840 pages

The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations.

Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted.

This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who like to enter this field.


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The New Mechanics of Myron Mathisson and Its Subsequent Development
Multipolar Test Body Equations of Motion in Generalized Gravity Theories
EnergyMomentum Tensors and Motion in Special Relativity
Solutions of MathissonPapapetrou Equations for Highly Relativistic Spinning Particles
The MPD Equations in Analytic Perturbative Form
Center of Mass Spin Supplementary Conditions and the Momentum of Spinning Particles
Theory and Experiment and the Role of Hidden Momentum
Equations of Motion of Schwarzschild ReissnerNordström and Kerr Particles
On the Selfforce in Electrodynamics and Implications for Gravity
Selfgravitating Elastic Bodies
On Geodesic Dynamics in Deformed BlackHole Fields
Higher Order PostNewtonian Dynamics of Compact Binary Systems in Hamiltonian Form
Spin and Quadrupole Contributions to the Motion of Astrophysical Binaries
Testing the Motion of Strongly SelfGravitating Bodies with Radio Pulsars
Equations of Motion in an Expanding Universe
The Galactic Center Black Hole Laboratory

From Singularities of Fields to Equations of Particles Motion
Motion of Spinless Particles in Gravitational Fields
On the Strong Field Point Particle Limit and Equation of Motion in General Relativity
Motion in Classical Field Theories and the Foundations of the Selfforce Problem
An Introduction to Gravitational SelfForce
Computational Strategies
Perspectives for Their Detection
Level Sets of the Lapse Function in Static GR
Aberrational Effects for Shadows of Black Holes
TimeDomain Inspiral Templates for Spinning Compact Binaries in QuasiCircular Orbits

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About the author (2015)

Bernard Schutz has done research and teaching in general relativity and especially its applications in astronomy since 1970. He is the author of more than 200 publications, including Geometrical Methods of Mathematical Physics and Gravity from the Ground Up (both published by Cambridge University Press). Schutz currently specialises in gravitational wave research, studying the theory of potential sources and designing new methods for analysing the data from current and planned detectors. He is a member of most of the current large-scale gravitational wave projects: GEO600 (of which he is a PI), the LIGO Scientific Collaboration, and LISA. Schutz is a Director of the Max Planck Institute for Gravitational Physics, also known as the Albert Einstein Institute (AEI), in Potsdam, Germany. He holds a part-time chair in Physics and Astronomy at Cardiff University, Wales, as well as honorary professorships at Potsdam and Hanover universities in Germany. Educated in the USA, he taught physics and astronomy for twenty years at Cardiff before moving to Germany in 1995 to the newly-founded AEI. In 1998 he founded the open-access online journal Living Reviews in Relativity. The Living Reviews family now includes six journals. In 2006 he was awarded the Amaldi Gold Medal of the Italian Society for Gravitation (SIGRAV), and in 2011 he received an honorary DSc from the University of Glasgow. He is a Fellow of the American Physical Society and the Institute of Physics, an Honorary Fellow of the Royal Astronomical Society, and a member of the Learned Society of Wales, the German Academy of Natural Sciences Leopoldina and the Royal Society of Arts and Sciences, Uppsala.

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