  Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the
twin paradox in Schwarzschild spacetime. Considering circular motion they
showed that the twin with a non-vanishing 4-acceleration is older than his
brother at the reunion and argued that in spaces that are asymptotically
Minkowskian there exists an absolute standard of rest determining which twin is
oldest at the reunion. Here we show that with vertical motion in Schwarzschild
spacetime the result is opposite: The twin with a non-vanishing 4-acceleration
is younger. We also deduce the existence of a new relativistic time effect,
that there is either a time dilation or an increased rate of time associated
with a clock moving in a rotating frame. This is in fact a first order effect
in the velocity of the clock, and must be taken into account if the situation
presented by Abramowicz and Bajtlik is described from the rotating rest frame
of one of the twins. Our analysis shows that this effect has a Machian
character since the rotating state of a frame depends upon the motion of the
cosmic matter due to the inertial dragging it causes. We argue that a
consistent formulation and resolution of the twin paradox makes use of the
general principle of relativity and requires the introduction of an extended
model of the Minkowski spacetime. In the extended model Minkowski spacetime is
supplied with a cosmic shell of matter with radius equal to its own
Schwarzschild radius, so that there is perfect inertial dragging inside the
shell.
