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GR: Fachverband Gravitation und Relativitätstheorie

GR 2: Classical Theory of General Relativity 1

GR 2.2: Vortrag

Montag, 30. März 2020, 12:00–12:15, H-HS IX

Relativistic Geodesy - Formalism and Concepts — •Dennis Philipp, Eva Hackmann, Volker Perlick, and Claus Lämmerzahl — ZARM, Universität Bremen

The Earth's geoid is one of the most important fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions within Einstein's theory of General Relativity is inevitable.

Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential as a generalization of known (post-) Newtonian notions. It is the same as realized by local plumb lines. Thereupon, the relativistic geoid is defined in direct analogy to the Newtonian understanding. Moreover, a generalized version of the so-called normal gravity field is presented. In the respective limits, well-known results are recovered.

A comparison between the Earth's Newtonian geoid and its relativistic generalization is a very subtle problem. However, an isometric embedding into Euclidean three-dimensional space can solve it and allows a genuinely intrinsic comparison of the general relativistic, the post-Newtonian, and the Newtonian concept. We employ this method and determine the leading-order differences, which are at the mm-level.