Energy Estimates and Gravitational Collapse

Abstract

We study the cancelations in the energy estimates for Einstein vacuum equations in order to prove the formation of black holes along evolutions. The novelty of the paper is that, we completely avoid using rotation vector fields to establish the global existence theorem of the solution. More precisely, we use only canonical null directions as commutators to derive energy estimates at the level of one derivatives of null curvature components.

2 figures, 40 pages

References in corpus (2)

• Strongly Focused Gravitational Waves
• On emerging scarred surfaces for the Einstein vacuum equations

Cited by in corpus (7)

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• Trapped surfaces in vacuum arising dynamically from mild incoming radiation
• Global solutions of nonlinear wave equations with large energy
• A Scale-Critical Trapped Surface Formation Criterion: A New Proof via Signature for Decay Rates
• A scale-critical trapped surface formation criterion for the Einstein-Maxwell system