A Scale-Critical Trapped Surface Formation Criterion: A New Proof via Signature for Decay Rates

Abstract

For gravitational collapse, we observe a correspondence between region close to past null infinity and region close to central singularity. In line with this philosophy, we construct a new ansatz, with which we first present a 40-page self-contained proof of trapped surface formation in a far-from-center region. A systematical approach with only signature for decay rates is used. Then by a rescaling argument, we convert this result into a reproof and an extension of a scale-critical theorem proved by An-Luk.

arXiv comment55 pages

References in corpus (8)

• A scattering theory construction of dynamical vacuum black holes
• A fully anisotropic mechanism for formation of trapped surfaces in vacuum
• Ultimately Schwarzschildean Spacetimes and the Black Hole Stability Problem
• Strongly Focused Gravitational Waves
• The intersection of a hyperplane with a lightcone in the Minkowski spacetime
• Energy Estimates and Gravitational Collapse
• Dynamical formation of black holes due to the condensation of matter field
• Formation of Trapped Surfaces from Past Null Infinity

Cited by in corpus (3)

• Anisotropic Dynamical Horizons Arising in Gravitational Collapse
• A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
• Construction of Cauchy data for the dynamical formation of apparent horizons and the Penrose Inequality