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

Abstract

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.