On a nonstatic Painleve-Gullstrand spacetime

TL;DR

This paper proposes a dynamic, spherically symmetric spacetime model with zero energy density but nonzero pressures, exploring its properties and implications for short measurement durations.

Contribution

It introduces a novel time-dependent geometry with zero energy density and analyzes its physical properties and behavior over different measurement times.

Findings

Physical quantities remain finite at all points.

Total energy flux on constant radius hypersurfaces is zero.

The effect of the mass source diminishes for very short times.

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.