Light Cone Structure near Null Infinity of the Kerr Metric

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.

References in corpus (8)

• Characteristic Evolution and Matching
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• Angular momentum conservation for dynamical black holes
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• Einstein equations in the null quasi-spherical gauge
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• Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates
• Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework
• On Newman-Penrose constants of stationary electrovacuum spacetimes
• Null hypersurface caustics and super-entropic black holes
• Shaving off soft hairs and the black hole image memory effect