Notes on the Sagnac effect in general relativity

  • Jörg FrauendienerEmail author
Research Article


The Sagnac effect can be described as the difference in travel time between two photons traveling along the same path in opposite directions. In this paper we explore the consequences of this characterisation in the context of General Relativity. We derive a general expression for this time difference in an arbitrary space-time for arbitrary paths. In general, this formula is not very useful since it involves solving a differential equation along the path. However, we also present special cases where a closed form expression for the time difference can be given. The main part of the paper deals with the discussion of the effect in a small neighbourhood of an arbitrarily moving observer in their arbitrarily rotating reference frame. We also discuss the special case of stationary space-times and point out the relationship between the Sagnac effect and Fizeau’s “aether-drag” experiment.


Sagnac effect Arbitrary moving reference frame Gravitational wave detection Frame dragging Fizeau experiment 



I wish to thank the CNRS of France for a visiting position at the Département de Mathématiques at Université de Bourgogne in Dijon, where some of this research was carried out. My thanks also go to Eyal Schwartz for sparking my interest in the Sagnac effect and to Niels Kjaergaard for pointing me to reference [12].


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  2. 2.Institut de Mathématiques de BourgogneUniversité de BourgogneDijonFrance

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