Towards exact relativistic theory of Earth's geoid undulation

Abstract

The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulate differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.

14 pages, no figures, several typos in equations, footnotes and bibliography were found and fixed

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• A strontium lattice clock with $3\times 10^{-17}$ inaccuracy and its frequency
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• Post-Newtonian reference-ellipsoid for relativistic geodesy
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• Normal gravity field in relativistic geodesy
• Potentials for general-relativistic geodesy
• General Relativity and Geodesy
• Relativistic geoids and time dependence: quasilocal frames versus isochronometric surfaces