Twin paradox on the photon sphere

Abstract

We consider another version of the twin paradox. The twins move along the same circular free photon path around the Schwarzschild center. In this case, despite their different velocities, all twins have the same nonzero acceleration. On the circular photon path, the symmetry between the twins situations is broken not by acceleration (as it is in the case of the classic twin paradox), but by the existence of an absolute standard of rest (timelike Killing vector). The twin with the higher velocity with respect to the standard of rest is younger on reunion. This closely resembles the case of periodic motions in compact (nontrivial topology) three-dimensional (3D) space recently considered in the context of the twin paradox by Barrow and Levin [Phys. Rev. A 63, 044104 (2001)], except that in that paper accelerations of all twins were equal to zero and that, in the case considered here, the 3D space has trivial topology.