Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates

Abstract

Using a quasi-spherical approximation of an affine-null metric adapted to an asymptotic Bondi inertial frame, we present high order approximations of the metric functions in terms of the specific angular momentum for a slowly rotating stationary and axi-symmetric vacuum spacetime. The metric is obtained by following the procedure of integrating the hierarchy of Einstein equations in a characteristic formulation utilizing master functions for the perturbations. It is further verified its equivalence with the Kerr metric in the slowly rotation approximation by carrying out an explicit transformation between the Boyer-Lindquist coordinates to the employed affine-null coordinates.

References in corpus (6)

• The affine-null formulation of the gravitational equations: spherical case
• Light Cone Structure near Null Infinity of the Kerr Metric
• Intrinsic angular momentum for radiating spacetimes which agrees with the Komar integral in the axisymmetric case
• The Bondi-Sachs metric at the vertex of a null cone: axially symmetric vacuum solutions
• Boosted Schwarzschild Metrics from a Kerr-Schild Perspective
• The Kerr-de Sitter spacetime in Bondi coordinates

Cited by in corpus (4)

• Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework
• Characteristic initial value problems for the Einstein-Maxwell-scalar field equations in spherical symmetry
• Conformal compactification and affine-null metric formulation of the Einstein equations
• Hierarchical formulation of the self-gravitating, n-dimensional, charged scalar field in spherical symmetry in affine null formalism