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