The Kerr-de Sitter spacetime in Bondi coordinates

TL;DR

This paper derives the Kerr-de Sitter metric in Bondi coordinates using null geodesics, explicitly expressing the metric components and setting the radial coordinate as the areal coordinate in Bondi-Sachs gauge.

Contribution

It provides a new explicit form of the Kerr-de Sitter metric in Bondi coordinates, facilitating studies of asymptotic properties and gravitational radiation.

Findings

Explicit metric components in Bondi coordinates

Radial coordinate set as areal coordinate

Asymptotic metric in Bondi-Sachs gauge

Abstract

We use zero angular momentum null geodesics in the Kerr-de Sitter spacetime to transform the metric in a generalised Bondi coordinate system. We write the metric components explicitly. Next, we choose the radial coordinate to be the areal coordinate and write the asymptotic metric in the Bondi-Sachs gauge.