Global conformal diagram of a black hole with angular momentum

Abstract

We present the first explicit global conformal diagram of Kerr spacetime and discuss some implications on the causal structure. For this construction we use a new double null coordinate system for Kerr spacetime, which we have recently presented. These null coordinates are smooth everywhere and are naturally adapted to the horizons and to the null infinities. In this setting there naturally appears a family of spheres that are parameterized by r s , which are the intersections of both null coordinates, and r s can be thought of as the extension of the tortoise coordinate for the Kerr spacetime.