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- 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