Numerical study of the Kerr solution in rotating coordinates

TL;DR

This paper numerically investigates the Kerr black hole solution in rotating coordinates using spectral methods, focusing on convergence behavior for various initial conditions and parameters.

Contribution

It introduces a numerical approach to construct the Kerr solution in corotating coordinates via spectral methods and analyzes convergence properties.

Findings

Successful numerical construction of Kerr solution in rotating coordinates.

Convergence depends on initial conditions and Kerr parameters.

Spectral method effectively solves Ernst equation for this setup.

Abstract

The Kerr solution in coordinates corotating with the horizon is studied as a testbed for a spacetime with a helical Killing vector in the Ernst picture. The solution is numerically constructed by solving the Ernst equation with a spectral method and a Newton iteration. We discuss convergence of the iteration for several initial iterates and different values of the Kerr parameters.