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Relativistic Geodesy pp 87–130Cite as

Measuring the Gravitational Field in General Relativity: From Deviation Equations and the Gravitational Compass to Relativistic Clock Gradiometry

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 196))

Abstract

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 method 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.

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Notes

  1. 1.

    We use “s” to indicate relations which only hold for symmetric connections and denote Riemannian objects by the overbar.

  2. 2.

    The contortion \(K_{y_2 y_1 y_3}\) should not be confused with the Jacobi propagator \(K^x{}_y\).

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Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through the grant PU 461/1-1 (D.P.). The work of Y.N.O. was partially supported by PIER (“Partnership for Innovation, Education and Research” between DESY and Universität Hamburg) and by the Russian Foundation for Basic Research (Grant No. 16-02-00844-A).

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Authors and Affiliations

  1. Theoretical Physics Laboratory, Nuclear Safety Institute, Russian Academy of Sciences, B. Tulskaya 52, 115191, Moscow, Russia

    Yuri N. Obukhov

  2. Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, 28359, Bremen, Germany

    Dirk Puetzfeld

Authors
  1. Yuri N. Obukhov
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  2. Dirk Puetzfeld
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Correspondence to Dirk Puetzfeld .

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Editors and Affiliations

  1. ZARM, University of Bremen, Bremen, Germany

    Dirk Puetzfeld

  2. ZARM, University of Bremen, Bremen, Germany

    Claus Lämmerzahl

Appendix

Appendix

1.1 A Directory of Symbols

Table 1 Directory of symbols
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Table 2 Directory of symbols (continued)
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Obukhov, Y.N., Puetzfeld, D. (2019). Measuring the Gravitational Field in General Relativity: From Deviation Equations and the Gravitational Compass to Relativistic Clock Gradiometry. In: Puetzfeld, D., Lämmerzahl, C. (eds) Relativistic Geodesy. Fundamental Theories of Physics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-030-11500-5_3

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