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The spacetimes for Vaidya's radiating stellar exterior and Kinnersley'sphoton rocket in a cosmological background are obtained by performing the sameconformal transformation as is used to obtain the Robertson-Walker metric fromMinkowski spacetime. In the case of the cosmological radiating stellarexterior, a two-fluid solution is found that obeys all of the energy conditionsand consists of a null fluid and a perfect fluid that asymptotically falls offto the standard cosmological values for pressure and density at infiniteradius. For the cosmological photon rocket, the massless case is firstinterpreted to obtain a solution for an accelerating cosmological referenceframe, and then the general case is interpreted: in both cases, a two-fluidsolution is found that consists of a null fluid and an imperfect fluid thatpossesses heat conduction and anisotropic stress. The imperfect fluid appearsto contain an inhomogeneous dark energy component that acts to accelerate thematter through space via a pressure gradient, but this component has negativeenergy density on the trailing side of the rocket, meaning only the leadingside of the rocket is guaranteed to satisfy the weak and dominant energyconditions. Unlike spacetimes that have rotation but no acceleration, thecosmological photon rocket can serve as an example of a spacetime thatcontradicts Mach's notion of acceleration, since an observer would seeempirical evidence of acceleration even though the matter does not acceleraterelative to the universe's background matter distribution.

Cosmological versions of Vaidya's radiating stellar exterior, an accelerating reference frame, and Kinnersley's photon rocket