Abstract
The question is discussed whether the description of the gravitational Doppler effect as a simple energy effect is consistent with its general-relativistic description as a metric-time effect. The difference between a local description and a global one is stressed. In the local description one is permitted to ignore metric effects. The global description yields a position-dependent rate of proper time in a gravitational field, and the energy, or the frequency, of a “freely falling” photon is described as a constant of motion. An experiment of nonlocal character measuring, simultaneously, the gravitational Doppler effect and the position-dependent rate of proper time may be performed by the use of a geostationary satellite. A simple general-relativistic treatment of the satellite experiment is obtained by transforming the Schwarzschild metric to a rotating frame, and describing the motion of free particles and the rates of standard clocks in the resulting metric.
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Grøn, Ø. The gravitational Doppler effect explored by means of a geostationary satellite. Found Phys 10, 567–579 (1980). https://doi.org/10.1007/BF00715040
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DOI: https://doi.org/10.1007/BF00715040