Abstract
The explicit form of the solutions of the Einstein field equations corresponding to a perfect fluid in geodesic, hypersurface-orthogonal motion is given with the following restrictions: (i) the comoving hypersurfaces are flat; and (ii) the second fundamental form of these surfaces is degenerate. These results are a natural extension of the metrics previously found by Szafron and co-workers [D. A. Szafron and J. Wainwright, J. Math. Phys. 18, 1668 (1977); D. A. Szafron, ibid. 18, 1673 (1977); D. A. Szafron and C. B. Collins, ibid. 20, 2354 (1979)] as a perfect fluid generalization of the Szekeres dust solutions.
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