Encyclopedia of Geodesy

Living Edition
| Editors: Erik Grafarend

Operational Significance of the Deviation Equation in Relativistic Geodesy

  • Dirk PuetzfeldEmail author
  • Yuri N. Obukhov
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-02370-0_164-1


Deviation equation. Second-order differential equation for the 4-vector which measures the distance between reference points on neighboring world lines in spacetime manifolds.

Relativistic geodesy. Science representing the Earth (or any planet), including the measurement of its gravitational field, in a four-dimensional curved spacetime using differential-geometric methods in the framework of Einstein’s theory of gravitation (general relativity).


How does one measure the gravitational field in Einstein’s theory? What is the foundation of relativistic gradiometry? The deviation equation gives answers to these fundamental questions.

In Einstein’s theory of gravitation, i.e., general relativity, the gravitational field manifests itself in the form of the Riemannian curvature tensor R abcd (Synge, 1960). This 4th-rank tensor can be defined as a measure of the noncommutativity of the parallel transport process of the underlying spacetime manifold (Synge and Schild, 1978...
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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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.ZARMUniversity of BremenBremenGermany
  2. 2.Theoretical Physics LaboratoryNuclear Safety Institute, Russian Academy of SciencesMoscowRussia