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GR: Fachverband Gravitation und Relativitätstheorie
GR 5: Classical Relativity
GR 5.3: Vortrag
Dienstag, 21. März 2023, 17:40–18:00, ZEU/0255
On the redshift and relativistic gravity potential determination in GR — •Dennis Philipp1,2, Eva Hackmann1,2, and Claus Laemmerzahl1,2 — 1ZARM, University of Bremen, 28359 Bremen, Germany — 2Gauss-Olbers Center, c/o ZARM, University of Bremen, 28359 Bremen, Germany
We derive exact, formal expressions for the relativistic redshift and timing between observers in various configurations on stationary spacetimes for the purpose of chronometry, i.e., relativistic gravimetry based on clocks. These observers are assumed to transport standard clocks along their respective worldlines and may move in an arbitrary way - on geodesics, accelerated, or are simply stationary. It is shown how redshift observations can be used to infer the (mass) multipole moments of the underlying spacetime, i.e., a decomposition of the gravito-electric potential. In particular, an Earth-bound observer is considered that is meant to model a standard clock on the Earth's surface (or on the geoid). Its clock is continuously compared to a satellite's clock to determine a relativistic gravity potential from redshift measurements. Results shown here are in agreement with the Newtonian potential determination from the so-called energy approach. The framework is intended for applications within relativistic geodesy and is applied in different exact vacuum spacetimes for illustration.