Formation of Trapped Surfaces from Spacelike Initial Data
arXiv:2607.11236
summary
The paper constructs specific short‑pulse spacelike initial data for Einstein’s equations and shows how these data can be extended to asymptotically flat Cauchy data, leading to the formation of trapped surfaces.
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}.
Topics & keywords
#trapped surfaces#spacelike initial data#short‑pulse method#asymptotically flat spacetimes#Cauchy problemfree data formalismlocal existenceCK25CK26Li‑Yu extension