Symmetries of asymptotically flat axisymmetric spacetimes with null dust

TL;DR

This paper investigates the symmetries of asymptotically flat, axisymmetric spacetimes with null dust, revealing that the only additional symmetries are supertranslational, leading to non-radiative gravitational fields.

Contribution

It demonstrates that in such spacetimes, the only extra symmetry compatible with null dust and asymptotic flatness is a supertranslational Killing vector, constraining the gravitational radiation.

Findings

Additional Killing vector is supertranslational

Gravitational field is non-radiative

Symmetry constraints limit gravitational radiation

Abstract

Symmetries of spacetimes with null dust field as a source compatible with asymptotic flatness are studied by using the Bondi-Sachs-van der Burg formalism. It is shown that in an axially symmetric spacetime with null dust field in which at least locally a smooth null infinity in the sense of Penrose exists, the only allowable additional Killing vector forming with the axial one a two-dimensional Lie algebra (the axial and the additional Killing vector are not assumed to be hypersurface orthogonal) is a supertranslational Killing vector and the gravitational field is then non-radiative (the Weyl tensor has a non-radiative character).