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406 25 Collision of plane wavessolutions which describe shells of null dust and impulsive or shock gravitationalwaves (Tsoubelis 1989). They contain the particular solution dueto Babala (1987), in which the interaction region is locally flat.The conclusion of Chandrasekhar and Xanthopoulos (1987a) was thatnull dust can be converted into stiff matter. Feinstein et al. (1989) arguedthat admissible field equations for the underlying physics of thematter should lead to appropriate boundary conditions at the null surfacesbounding the interaction region, and thus to an unambiguous answerfor the combined gravitational and matter system: this is related touniqueness for the characteristic initial value problem. It is true for e.g.Maxwell fields and scalar fields of the usual type, although one can constructmacroscopic models whose governing equations do not have thisproperty (Hayward 1990).Models of colliding shells accompanied by gravitational waves of nulldust can be derived from the vacuum solution (25.26) (Tsoubelis andWang 1990). Cosmological aspects of the interaction of null fluids arediscussed by Letelier and Wang (1993). With the aid of the inversescattering method and the Kaluza–Klein dimension reduction, Cruzateet al. (1988) were able to find solutions describing the collision of solitonsin a FRW background with the equation of state p =(γ −1)µ. FerrariandIbañez (1989) used the same techniques and obtained, in the interactionregion of null fields, a solution with the source term of an anisotropicfluid.Feinstein and Senovilla (1989a) found an exact solution for the collisionof a variably polarized wave with (across the null boundaries) anarbitrarily smooth wave front and a shell of null dust followed by a planegravitational wave with constant polarization. In the Szekeres form (25.5)of the metric, the solution is given byds 2 = −2f u g v W −3/8 e R(v) dudv + W 1/2 [W dy 2 +(dx − ω(v)dy) 2 ],(25.74)W = f(u)+g(v), ω 2 v =2R v g v ,where f(u) and two of the three functions g(v), R(v), ω(v) can be freelychosen.