Event horizon gluing and black hole formation in vacuum: the very slowly rotating case

TL;DR

This paper develops a nonperturbative method for gluing Minkowski space to black hole horizons in vacuum, enabling the construction of vacuum gravitational collapse to slowly rotating Kerr black holes and the first example of a spacelike singularity from vacuum collapse.

Contribution

It introduces a new characteristic gluing technique in vacuum that allows for precise control of initial data leading to black hole formation and singularity development.

Findings

Minkowski space can be glued to Schwarzschild horizons as a $C^2$ solution.

Constructs vacuum collapse to very slowly rotating Kerr black holes.

First example of a spacelike singularity from vacuum gravitational collapse.

Abstract

In this paper, we initiate the study of characteristic event horizon gluing in vacuum. More precisely, we prove that Minkowski space can be glued along a null hypersurface to any round symmetry sphere in a Schwarzschild black hole spacetime as a $C^2$ solution of the Einstein vacuum equations. The method of proof is fundamentally nonperturbative and is closely related to our previous work in spherical symmetry [KU22] and Christodoulou's short pulse method [Chr09]. We also make essential use of the perturbative characteristic gluing results of Aretakis-Czimek-Rodnianski [ACR21a; CR22]. As an immediate corollary of our methods, we obtain characteristic gluing of Minkowski space to the event horizon of very slowly rotating Kerr with prescribed mass $M$ and specific angular momentum $a$. Using our characteristic gluing results, we construct examples of vacuum gravitational collapse to very slowly rotating Kerr black holes in finite advanced time with prescribed $M$ and $0\le |a|\ll M$. Our construction also yields the first example of a spacelike singularity arising from one-ended, asymptotically flat gravitational collapse in vacuum.