A class of self-similar perfect-fluid spacetimes, and a generalisation

Abstract

Many previous studies of general relativistic perfect fluids have been assumed that the geometry is hypersurface homogeneous. With the additional requirement of self-similarity, this leads to solutions which are invariant under a similarity group that acts transitively on the entire spacetime. The authors investigate the 'simplest' self-similar situations where this is not the case. The spacetimes admit a four-parameter similarity group, whose orbits are spacelike hypersurfaces which are orthogonal to the fluid flow. They also introduce a generalisation of the notion of self-similarity. In the analogous 'simplest' case, they consider all possible solutions in a unified manner, for a fluid which obeys a barotropic equation of state. The authors' discussion of the entire class enables them to obtain all accelerating solutions in closed form and serves to characterise several previous studies in a geometrically invariant way, thereby shedding light on their interconnections.