Light Cone Structure near Null Infinity of the Kerr Metric

TL;DR

This paper investigates the null infinity structure of the Kerr metric, constructing shearfree null hypersurfaces, analyzing its asymptotic geometry, and computing Newman-Penrose constants, which are found to be zero, with implications for gravitational radiation.

Contribution

It develops a detailed asymptotic analysis of the Kerr metric near null infinity, including the construction of shearfree hypersurfaces and the calculation of Newman-Penrose constants.

Findings

Null hypersurfaces intersect null infinity in shearfree cuts.

The Kerr metric's Newman-Penrose constants are zero.

The asymptotic structure of Kerr near null infinity is characterized.

Abstract

Motivated by our attempt to understand the question of angular momentum of a relativistic rotating source carried away by gravitational waves, in the asymptotic regime near future null infinity of the Kerr metric, a family of null hypersurfaces intersecting null infinity in shearfree (good) cuts are constructed by means of asymptotic expansion of the eikonal equation. The geometry of the null hypersurfaces as well asthe asymptotic structure of the Kerr metric near null infinity are studied. To the lowest order in angular momentum, the Bondi-Sachs form of the Kerr metric is worked out. The Newman-Unti formalism is then further developed, with which the Newman-Penrose constants of the Kerr metric are computed and shown to be zero. Possible physical implications of the vanishing of the Newman-Penrose constants of the Kerr metric are also briefly discussed.