xx ShiftedKerrSchild

ShiftedKerrSchild

Zacharia E. Etienne <zachetie *at* gmail *dot* com> Roland Haas <rhaas@illinois.edu>

November 04 2019

Abstract

To set up Kerr-Schild initial data, with a shifted radial coordinate.

1 Introduction

A complete description of a black hole spacetime in Kerr-Schild spherical polar coordinates that includes an explicit analytic form of the extrinsic curvature for arbitrary spin parameters does not exist in the literature, so we first include it here for completeness. Then we present our strategy for transforming spacetime quantities into shifted Kerr-Schild Cartesian coordinates.

2 Physical System In unshifted spherical polar coordinates, where , is the black hole mass, and is the black hole spin parameter, the Kerr-Schild lapse, shift, and 3-metric are given by