A Class of Type [4] Perfect Fluid Space-Times

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Abstract
The existence of gravitational fields of Petrov‐Penrose type [4] in the presence of a perfect fluid is established. In particular, the general type [4] solution of the Einstein field equations with a perfect fluid as source is obtained subject to the restriction that the repeated principal null congruence of the Weyl tensor is geodesic. The line element is expressed in terms of four arbitrary functions of a single variable, and in general admits no Killing vectors. The fluid flow is irrotational, but has nonzero shear, expansion, and acceleration. The physically reasonable requirement 0 < p ≤ A, where p is the fluid pressure and A the rest energy density, is imposed, and restricts the domain of validity of the solutions to a certain extent. In addition, it is shown that the stronger condition 0 < p ≤ A/3 excludes certain of the above solutions and further restricts the domain of validity of the remaining ones.

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