Conformal time dependent Painleve-Gullstrand spacetime
arXiv:1202.2285
Abstract
The properties of an anisotropic fluid outside a star or a black hole embedded in an expanding universe are investigated. One finds that, in Painleve-Gullstrand coordinates, the heat flux of the cosmological fluid vanishes, in spite of the nonzero value of a non-diagonal component of the stress tensor. The pressures and energy density of the fluid are regular at , divergent at and change sign at certain values of their arguments.
8 pages, no figures, one chapter added, new refs