  The spacetimes for Vaidya's radiating stellar exterior and Kinnersley's
photon rocket in a cosmological background are obtained by performing the same
conformal transformation as is used to obtain the Robertson-Walker metric from
Minkowski spacetime. In the case of the cosmological radiating stellar
exterior, a two-fluid solution is found that obeys all of the energy conditions
and consists of a null fluid and a perfect fluid that asymptotically falls off
to the standard cosmological values for pressure and density at infinite
radius. For the cosmological photon rocket, the massless case is first
interpreted to obtain a solution for an accelerating cosmological reference
frame, and then the general case is interpreted: in both cases, a two-fluid
solution is found that consists of a null fluid and an imperfect fluid that
possesses heat conduction and anisotropic stress. The imperfect fluid appears
to contain an inhomogeneous dark energy component that acts to accelerate the
matter through space via a pressure gradient, but this component has negative
energy density on the trailing side of the rocket, meaning only the leading
side of the rocket is guaranteed to satisfy the weak and dominant energy
conditions. Unlike spacetimes that have rotation but no acceleration, the
cosmological photon rocket can serve as an example of a spacetime that
contradicts Mach's notion of acceleration, since an observer would see
empirical evidence of acceleration even though the matter does not accelerate
relative to the universe's background matter distribution.
