On a star with expanding isotropic fluid

The generalized Gullstrand-Painleve geometry is investigated for expanding matter. Compared to other studies, we take into account an anisotropic stress tensor as the source of curvature with an equation of state resembling the MIT bag model form. The spacetime becomes de Sitter for $t>>1\mathrm{/}\sqrt{\mathrm{\Lambda }},\mathrm{\Lambda }$ being the equivalent cosmological constant. The energy density and pressures of the fluid are only time dependent but the scalar curvature is constant. The radial geodesics are computed.