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We extend the Vaidya radiating metric to include both a radiation field and a string fluid. Assuming diffusive transport for the string fluid, we find new analytic solutions of Einstein's field equations. Our new solutions represent an extention of Xanthopoulos superposition.

We have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid. This paper expands our brief introduction to extensions of the Schwarzschild vacuum which appeared in 1998 Phys. Rev. D 57 R5945. Assuming diffusive transport for the string fluid, we find new analytic solutions of Einstein's field equations.

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Spherically symmetric perfect fluids are studied under the restriction of shear-free motion. All solutions of the field equations are found by solving a single second order nonlinear equation containing an arbitrary function. It is shown that this arbitrary function is a geometric invariant, E, which measures the gravitational field energy, and it is shown that E=const generates all the homogeneous density solutions. An improved proof is given for the nonexistence of any one-parameter equation of state. A number of exact solutions are presented and discussed.