Physical infeasibility of geodesic dissipative dust as a source of gravitational radiation

TL;DR

This paper demonstrates that a geodesic, dissipative, rotational dust source cannot produce gravitational radiation unless it reduces to a non-dissipative, non-rotating FRW universe, due to regularity conditions.

Contribution

It proves the physical infeasibility of geodesic dissipative dust as a gravitational radiation source under symmetry and regularity constraints.

Findings

Dissipative flux must vanish for regularity at the center.

Vorticity must vanish unless dissipative flux is zero.

Resulting spacetime reduces to FRW, which does not emit gravitational waves.

Abstract

Using a framework based on the 1+3 formalism, we show that a source represented by a geodesic, dissipative, rotational dust, endowed with axial and reflection symmetry, violates regularity conditions at the center of the fluid distribution, unless the dissipative flux vanishes. In this latter case the vorticity also must vanish, and the resulting spacetime is Friedman--Robertson--Walker (FRW). Therefore it does not produce gravitational radiation.