From the 1 of 9 linked papers with an AI index.
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Formation of Trapped Surfaces from Spacelike Initial Data
Xuantao Chen, Sergiu Klainerman
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 th…
A Physical space derivation of Morawetz-Energy estimates in Kerr spacetimes with large angular momentum
Lili He, Sergiu Klainerman
We revisit the derivation of Morawetz--energy estimates for scalar wave equations in the domain of outer communication of a Kerr spacetime \(\KK(a,m)\). Our goal is to develop robu…
Forward Construction of Vacuum Initial Data with Borderline Decay
Xuantao Chen, Sergiu Klainerman
We make use of the free data formalism developed in \cite{CK25} to construct solutions of the Einstein vacuum constraint equations by integrating in the forward direction. This, to…
Solving the constraint equation for general free data
Xuantao Chen, Sergiu Klainerman
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical…
A canonical foliation on null infinity in perturbations of Kerr
Sergiu Klainerman, Dawei Shen, Jingbo Wan
Kerr stability for small angular momentum has been proved in the series of works by Klainerman-Szeftel, Giorgi-Klainerman-Szeftel and Shen. Some of the most basic conclusions of th…
Formation of Trapped Surfaces in Geodesic Foliation
Xuantao Chen, Sergiu Klainerman
We revisit the classical results of the formation of trapped surfaces for the Einstein vacuum equation relying on the geodesic foliation, rather than the double null foliation used…