The motion of point particles in curved spacetime

This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle -- its only effect is to contribute to the particle's inertia. What remains after subtraction is a smooth field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free (radiative) field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (part II). It continues with a thorough discussion of Green's functions in curved spacetime (part III). The review concludes with a detailed derivation of each of the three equations of motion (part IV).Comment: LaTeX2e, 116 pages, 10 figures. This is the final version, as it will appear in Living Reviews in Relativit

Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry

How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity, can be obtained by means of two different methods. The first method relies on the measuring the accelerations of a suitably prepared set of test bodies relative to the observer. The second methods utilizes a set of suitably prepared clocks. The methods discussed here form the basis of relativistic (clock) gradiometry and are of direct operational relevance for applications in geodesy.Comment: To appear in "Relativistic Geodesy: Foundations and Application", D. Puetzfeld et. al. (eds.), Fundamental Theories of Physics, Springer 2018, 52 pages, in print. arXiv admin note: text overlap with arXiv:1804.11106, arXiv:1511.08465, arXiv:1805.1067

A spacetime description of relativistic media

discussion is given of relativistic balance laws that may be used to construct models of material media with spin and electromagnetic properties, interacting with general background electromagnetic fields and gravitation described by non-Riemannian geometries. The general framework offers an approximation scheme for modelling relativistic media by supplementing the balance laws with conditions that convert them into an involutive differential system