ON EXACT-SHEARING PERFECT-FLUID SOLUTIONS OF THE NONSTATIC SPHERICALLY SYMMETRICAL EINSTEIN FIELD-EQUATIONS

In this paper we have sought solutions of the nonstatic spherically symmetric field equations that exhibit nonzero shear. The Lorentzian-warped product construction is used to present the spherically symmetric metric tensor in double-null coordinates. The field equations, kinematical quantities, and Riemann invariants are computed for a perfect-fluid stress-energy tensor. For a special observer, one of the field equations reduces to a form that admits wavelike solutions. Assuming a functional relationship between the metric coefficients, the remaining field equation becomes a second-order nonlinear differential equation that may be reduced as well.