The gravitational Aharonov–Bohm effect with photons

The analogy between general relativity and electromagnetism suggests that there is a gravitational analog of the Aharonov–Bohm effect. There is indeed such an effect. Since gravitation couples to all fields, the effect should exist for photons. There is a close connection with the Sagnac effect. Both the electromagnetic field and the gravitational field are classical fields, so the effect could have been predicted in the interval between the publication of the theory of general relativity in 1915 and the discovery of quantum mechanics in the mid 1920s.