Local existence in a class of characteristic problems for the Einstein vacuum equations

TL;DR

This paper aimed to establish local existence results for characteristic problems in Einstein vacuum equations but was withdrawn due to a critical error in the proof, with a corrected version pending.

Contribution

The paper attempted to extend local existence theory for Einstein vacuum equations in characteristic settings, though it was withdrawn before completion.

Findings

The original proof contained an error in applying the Cauchy-Kowalevski theorem.

The main theorem (4.1) was not valid as initially claimed.

The paper was withdrawn and no conclusive results were published.

Abstract

This paper has been withdrawn by the author due to an error in the use of the Cauchy-Kowalevski theorem in section 4., theorem 4.1 which does not allow to prove the final result. When (and if) this error will be cured it will be replaced by a corrected version of the result.