Spacetimes with No Position Drift

Abstract

This paper compares three criteria for a spacetime to be free of position drift: those by Hasse and Perlick (HP), Krasi\'nski and Bolejko (KB) and Korzy\'nski and Kopi\'nski (KK). A spacetime having no position drift means that every observer sees all light sources in unchanging directions. The following is shown: (1) The HP criterion is a necessary condition for the KK criterion to apply. (2) If the spacetime metric obeys the Einstein equations with a perfect fluid source, then another necessary condition for the KK criterion is the Weyl tensor being zero. (3) Result (2) points to the Stephani metric, so it is shown that this metric obeys an equation which is still one more necessary condition for the KK criterion. (4) The general Szekeres metrics become drift-free by the KK criterion only in the Friedmann limit. (5) The HP and KB criteria coincide, and the HP zero-drift condition imposes on the Stephani metric the same restriction as found by Krasi\'nski and Bolejko (KB). The relations between the three criteria are displayed and compared in a diagram.