Teukolsky方程、扭函数与共形自对偶空间

IF 1.4 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Bernardo Araneda
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引用次数: 0

摘要

我们证明了具有自对偶Weyl张量的黎曼流形在任意共形和自旋权的Teukolsky方程解与扭函数之间的对应关系。特别地,我们给出了Teukolsky方程解的轮廓积分公式,并找到了一个递归算子,它产生无限族的解,并导致在扭转空间上构造Čech表示和串上同调类。除了一般的共形自对偶情况,例子包括自对偶黑洞,标量平面Kähler表面和quaternionic-Kähler度量,其中我们将Teukolsky方程映射到共形波动方程,建立与线性化Przanowski方程的新关系,并发现新的四元数变形类别。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Teukolsky equations, twistor functions, and conformally self-dual spaces

We prove a correspondence, for Riemannian manifolds with self-dual Weyl tensor, between twistor functions and solutions to the Teukolsky equations for any conformal and spin weights. In particular, we give a contour integral formula for solutions to the Teukolsky equations, and we find a recursion operator that generates an infinite family of solutions and leads to the construction of Čech representatives and sheaf cohomology classes on twistor space. Apart from the general conformally self-dual case, examples include self-dual black holes, scalar-flat Kähler surfaces, and quaternionic-Kähler metrics, where we map the Teukolsky equation to the conformal wave equation, establish new relations to the linearised Przanowski equation, and find new classes of quaternionic deformations.

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来源期刊
Letters in Mathematical Physics
Letters in Mathematical Physics 物理-物理:数学物理
CiteScore
2.40
自引率
8.30%
发文量
111
审稿时长
3 months
期刊介绍: The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.
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