English

On periodic solutions of nonlinear wave equations, including Einstein equations with a negative cosmological constant

General Relativity and Quantum Cosmology 2023-04-25 v2 High Energy Physics - Theory Mathematical Physics Analysis of PDEs Differential Geometry math.MP

Abstract

Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions of the vacuum, or of the Einstein-Maxwell-dilaton-scalar fields-Yang-Mills-Higgs-Chern-Simons-f(R)f(R) equations, with a negative cosmological constant." However, there is a gap in the proof, and it is unlikely that the strategy presented can be upgraded to a full proof.

Keywords

Cite

@article{arxiv.1711.11261,
  title  = {On periodic solutions of nonlinear wave equations, including Einstein equations with a negative cosmological constant},
  author = {Piotr T. Chruściel},
  journal= {arXiv preprint arXiv:1711.11261},
  year   = {2023}
}

Comments

From the author: this is the same file as the original submission, but the reader is warned that the proof contains a gap