On a nonstatic Painleve-Gullstrand spacetime

Abstract

A time dependent geometry outside a spherically symmetric mass is proposed. The source has zero energy density but nonzero radial and tangential pressures. The time variable is interpreted as the duration of measurement performed upon the physical system. For very short time intervals, the effect of the mass source is much reduced, going to zero when $t \rightarrow 0$. All physical quantities are finite when $t \rightarrow 0$ and $r \rightarrow 0$ and also at infinity. The total energy flux measured on a hypersurface of constant $r$ is vanishing.