Kerr-NUT-(A)de Sitter 及相关度规的时空刻画
广义相对论与量子宇宙学
2016-12-20 v3 微分几何
摘要
在 admitting 一个 Killing 矢量的四维 -真空时空中，通过自对偶 Weyl 张量与由该 Killing 矢量构造的自然自对偶双重二形式的成比例性，获得了 Kerr-NUT-(A)de Sitter 度规的刻画。这一结果恢复并扩展了先前对 Kerr 和 Kerr-NUT 度规的刻画。证明方法基于：(i) 存在第二个 Killing 矢量场，其完全由源自前一个 Killing 矢量的几何信息构建而成；(ii) 存在一个有趣的底层几何结构，涉及共形相关度规的黎曼淹没，这两者可能具有独立意义。
引用
@article{arxiv.1307.5018,
title = {A spacetime characterization of the Kerr-NUT-(A)de Sitter and related metrics},
author = {Marc Mars and José M. M. Senovilla},
journal= {arXiv preprint arXiv:1307.5018},
year = {2016}
}
备注
43 pages. No figures. v2: Statement of main theorem added in the Introduction. Section 4 divided into subsections. Minor additional changes. v3: Theorems 1 and 6 corrected to include a hypothesis that was not made explicit in version v1 and v2 and in the published paper. Relevant changes are highlighted in blue color. Some typos also amended