The essential self-adjointness of the wave operator on radiative spacetimes

Fuente: arXiv
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Autores principales: Jia, Qiuye, Molodyk, Mikhail, Sussman, Ethan
Formato: Preprint
Publicado: 2024
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author Jia, Qiuye
Molodyk, Mikhail
Sussman, Ethan
author_facet Jia, Qiuye
Molodyk, Mikhail
Sussman, Ethan
contents We prove the essential self-adjointness of the d'Alembertian $\square_g$, allowing a larger class of spacetimes than previously considered, including those that arise from perturbing Minkowski spacetime by gravitational radiation. We emphasize the fact, proven by Taira in closely related settings, that all tempered distributions $u$ satisfying $\square_g u = λu +f$ for $λ\in \mathbb{C}\backslash \mathbb{R}$ and $f$ Schwartz are Schwartz. The proof is fully microlocal and relatively quick given the ``de,sc-'' machinery recently developed by the third author.
format Preprint
id arxiv_https___arxiv_org_abs_2412_03828
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The essential self-adjointness of the wave operator on radiative spacetimes
Jia, Qiuye
Molodyk, Mikhail
Sussman, Ethan
Spectral Theory
General Relativity and Quantum Cosmology
Mathematical Physics
Analysis of PDEs
Primary 35L05, 35P05. Secondary 58J47, 58J50
We prove the essential self-adjointness of the d'Alembertian $\square_g$, allowing a larger class of spacetimes than previously considered, including those that arise from perturbing Minkowski spacetime by gravitational radiation. We emphasize the fact, proven by Taira in closely related settings, that all tempered distributions $u$ satisfying $\square_g u = λu +f$ for $λ\in \mathbb{C}\backslash \mathbb{R}$ and $f$ Schwartz are Schwartz. The proof is fully microlocal and relatively quick given the ``de,sc-'' machinery recently developed by the third author.
title The essential self-adjointness of the wave operator on radiative spacetimes
topic Spectral Theory
General Relativity and Quantum Cosmology
Mathematical Physics
Analysis of PDEs
Primary 35L05, 35P05. Secondary 58J47, 58J50
url https://arxiv.org/abs/2412.03828