Formation of the Kerr black hole: an exact model

Abstract

We present an exact analytical model of axisymmetric gravitational collapse leading to the formation of the Kerr black hole. The model depends only on the total mass ${\cal M}$ and a time dependent rotation parameter $a(v)$, and incorporates both the extremal Kerr black hole and a novel quasi extremal regime without requiring $a\approx{\cal M}$. The evolution develops curvature singularities induced by $a(v)$, which are expected to remain enclosed within a trapped region close to the evolving Kerr radius $r=h(v)$. It also predicts a transient anisotropic exterior curvature decaying as $1/r^2$, which may imprint observable signatures associated with the formation of a rotating black hole. The present construction should therefore be interpreted as an exact analytical description of the final stage of rotational gravitational collapse, immediately preceding the formation of the Kerr black hole.