Towards exact relativistic theory of Earth's geoid undulation
General Relativity and Quantum Cosmology
2021-03-30 v6 Geophysics
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.
Cite
@article{arxiv.1411.4205,
title = {Towards exact relativistic theory of Earth's geoid undulation},
author = {Sergei Kopeikin and Elena Mazurova and Alexander Karpik},
journal= {arXiv preprint arXiv:1411.4205},
year = {2021}
}
Comments
14 pages, no figures, several typos in equations, footnotes and bibliography were found and fixed