Formation of Trapped Surfaces from Spacelike Initial Data

Xuantao Chen; Sergiu Klainerman

Formation of Trapped Surfaces from Spacelike Initial Data

General Relativity and Quantum Cosmology 2026-07-13 v1 Analysis of PDEs Differential Geometry

Authors: Xuantao Chen , Sergiu Klainerman

Abstract

We make use of the free data formalism developed in \cite{CK25,CK26} to provide a direct construction of short-pulse type Cauchy data. The construction of the spacelike short-pulse follows from the local existence result established in \cite{CK26}. The forward integration construction in \cite{CK26} allows us to show that such data can be extended to a set of asymptotically flat Cauchy data. This greatly extends the result of Li--Yu \cite{LiYu}.

Cite

@article{arxiv.2607.11236,
  title  = {Formation of Trapped Surfaces from Spacelike Initial Data},
  author = {Xuantao Chen and Sergiu Klainerman},
  journal= {arXiv preprint arXiv:2607.11236},
  year   = {2026}
}