Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-04-07
Gen. Rel. Grav. 36, 2289 (2004)
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
26 pages, including 4 figures, corrected typos, changed references
Scientific paper
10.1023/B:GERG.0000046184.03333.
We present exact expressions for the Sagnac effect of Goedel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Goedel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.
Delgado Antonio
Kajari Endre
Schleich Wolfgang P.
Walser Reinhold
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