Physics
Scientific paper
Apr 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998cqgra..15.1043s&link_type=abstract
Classical and Quantum Gravity, Volume 15, Issue 4, pp. 1043-1062 (1998).
Physics
7
Scientific paper
Some years ago, it was conjectured that general relativistic shear-free perfect fluids, with a barotropic equation of state such that 0264-9381/15/4/024/img1, must be either expansion-free or irrotational. In this paper we present a fully covariant approach to this conjecture by using the so-called hydrodynamical formalism. We discuss the role of the variables and equations and the procedure for using them in a profitable way. We illustrate the method by giving the proof of the conjecture in two particular cases: (i) when the expansion and the energy density are functionally dependent, i.e. the case studied previously by Lang and Collins using the tetrad formalism; and (ii) when the expansion and the rotation scalar are functionally dependent, a case not treated hitherto.
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