Dynamical Formation of Black Holes due to Boundary Effect in Vacuum Gravity

TL;DR

This paper demonstrates that black holes can form dynamically in vacuum spacetimes due to boundary effects, without matter collapse, by establishing the formation of marginally outer trapped surfaces through boundary conditions and focusing mechanisms.

Contribution

It introduces a novel mechanism for black hole formation via boundary effects in vacuum gravity, expanding understanding beyond traditional matter collapse scenarios.

Findings

MOTS can form from boundary effects in vacuum spacetime.

A focusing mechanism can trigger MOTS formation without initial trapped surfaces.

Boundary generalized mean curvature condition is key to interior MOTS existence.

Abstract

We prove that a marginally outer trapped surface (MOTS) can form as a result of Einsteinian evolution in pure vacuum spacetime starting from regular initial data free of MOTSs due to pure boundary effects. We adapt a Cauchy-double-null framework and use the boundary generalized mean curvature condition for the existence of an interior MOTS imposed by the author S-T Yau in \cite{yau}. In particular, we prove that the condition of \cite{yau} can be met dynamically starting from a configuration that does not verify the same through a focusing mechanism. In fact, a very mild incoming radiation can cause a large enough generalized boundary mean curvature of an isotropically large domain so that a MOTS exists in the interior. This is fundamentally different from black hole formation by standard ``gravitational collapse" and can be interpreted as the dynamical realization of a long-suspected idea in GR: MOTS can form because of ``global geometry", not just quasi-local concentration of gravity/matter.