  We consider a new 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 non-zero
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 (non-trivial topology) 3-D space recently considered in the
context of the twin paradox by Barrow and Levin, except that there
accelerations of all twins were equal to zero, and that in the case considered
here, the 3-D space has trivial topology.
