Homothetic motions in general relativity

Abstract

Properties of homothetic or self-similar motions in general relativity are examined with particular reference to vacuum and perfect-fluid space-times. The role of the homothetic bivector with componentsH [a;b] formed from the homothetic vectorH is discussed in some detail. It is proved that a vacuum space-time only admits a nontrivial homothetic motion if the homothetic vector field is non-null and is not hypersurface orthogonal. As a subcase of a more general result it is shown that a perfect-fluid space-time cannot admit a nontrivial homothetic vector which is orthogonal to the fluid velocity 4-vector.