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

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.