Mathematics – Logic
Scientific paper
Mar 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cqgra..16..919b&link_type=abstract
Classical and Quantum Gravity, Volume 16, Issue 3, pp. 919-926 (1999).
Mathematics
Logic
4
Scientific paper
Some years ago Stephani derived two classes of rotating dust solutions. In this paper Stephani's results are generalized to the case where the cosmological constant 0264-9381/16/3/020/img1 is non-zero. The solutions are of Petrov type D and the magnetic part of the Weyl tensor vanishes. The solutions involve seven arbitrary functions of a spacelike coordinate and, in general, they admit no Killing vectors. Nevertheless the spacetime geometry is relatively simple and admits a foliation of timelike hypersurfaces of constant intrinsic curvature 0264-9381/16/3/020/img2 and zero extrinsic curvature. The (geodesic) flow-lines of the fluid are tangent to these hypersurfaces and, in general, the flow is rotating, shearing and expanding. In the vacuum limit the solutions reduce to spacetimes of constant curvature.
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