Frozen time in hyperbolic spacetime motion
  According to the Lorentz transformation and clearly seen from the Minkowski diagram, hyperbolic spacetime motion of a test object relative to a stationary reference frame can be performed in a specific way such that time becomes frozen in the moving frame of the test object. In that case, time can be arranged to become frozen even at moderate relativistic velocities, in contrast to the minute traditional relativistic time dilation at such velocities. An appendix gives a simple illustration in Minkowski form of how time in a frame in hyperbolic motion can become frozen to a complete standstill relative to a stationary frame. (Published in Phys. Scr. 84 (2011) 035004)   In addition to the paper, the arXiv file also contains a discussion of Frequently Asked Questions from readers. Further questions not adequately dealt with in the existing FAQ are welcome. 
Arne Bergstrom
physics.gen-ph