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The problem of two stiff fluids (energy density = pressure) moving radiallyin spherical symmetry is treated. The metric ansatz is chosen sphericallysymmetric, conformally static with a multiplicative separation of variables.The first fluid is described mathematically via a massless scalar field. Thecoordinate system is chosen comoving with the second fluid which the separationof variables requires to be stiff too. The fluids are interacting onlygravitationally and their energy momentum tensors are separately conserved. TheEinstein equations are reduced to a single nonlinear ODE of second order whichis shown to lead to an Abel ODE. A few particular exact solutions were foundusing a polynomial ansatz. The two non-comoving gravitational sources in thesolutions can be interpreted either as scalar fields or stiff fluids. Acomplete analysis is performed on the range of parameters for which the stifffluid interpretation is physically acceptable. General formulas are derived forthe conformal vectors of the solutions. By making the second fluid vanish, afew single scalar field solutions are generated some of which appear to be new.All solutions considered in this paper have a time-like singularity at theorigin (except the trivial FRW one) and are not asymptotically flat (except thestatic one with k=0).

Two non-comoving stiff fluids in radial motion and spherical symmetry