Energy Estimates and Gravitational Collapse

TL;DR

This paper develops a new method for analyzing Einstein vacuum equations, avoiding rotation vector fields, to prove black hole formation through energy estimates based solely on null directions.

Contribution

It introduces a novel approach using only canonical null directions for energy estimates, bypassing the need for rotation vector fields.

Findings

Proves black hole formation along evolutions.

Establishes global existence without rotation vector fields.

Uses null directions as the primary tool for energy estimates.

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.