自对偶黑洞的 incidence 关系
Incidence Relations for Self-Dual Black Holes
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中文总结 AI 辅助
研究在克尔-席尔德坐标下构造埃古奇-汉森、自对偶陶布-纽特等自对偶黑洞时空的incidence关系，借助杜南斯基-梅森递归求出普莱班斯基标量得到闭式公式，还简要勾勒了该背景下零质量场的构造。
中文摘要 AI 辅助
在彭罗斯的非线性引力子构造中，自对偶时空源于弯曲扭量空间中全纯扭量线的模空间，其显式参数化由 incidence 关系具体给出。我们在克尔-席尔德坐标下给出自对偶黑洞时空 incidence 关系的具体局域构造，涉及的时空包括：埃古奇-汉森（Eguchi-Hanson）时空、自对偶陶布-纽特（self-dual Taub-NUT）时空以及自对偶普莱班斯基-杰米亚斯基（self-dual Plebański-Demiański）时空。该构造借助普莱班斯基第二 heavenly 方程框架下的杜南斯基-梅森（Dunajski-Mason）递归实现，我们为此明确求出了普莱班斯基标量，所得结果为闭式公式。值得注意的是，自对偶陶布-纽特解的精确 incidence 关系对引力耦合呈现线性依赖关系。作为应用，我们简要勾勒了自对偶黑洞背景上零质量场的构造。
英文摘要
In Penrose's nonlinear graviton construction, a self-dual spacetime arises as the moduli space of holomorphic twistor lines in curved twistor space, whose explicit parametrization is concretely given by the incidence relation. We demonstrate a concrete local construction of the incidence relations for self-dual black hole spacetimes in Kerr-Schild coordinates: Eguchi-Hanson, self-dual Taub-NUT, and self-dual Plebański-Demiański. This is facilitated by implementing the Dunajski-Mason recursion in the framework of Plebański's second heavenly equation, for which we explicitly find the Plebański scalar. Our results describe closed-form formulae. Notably, for the self-dual Taub-NUT solution, the exact incidence relation exhibits linear dependence on the gravitational coupling. The construction of zero-rest-mass fields on self-dual black hole backgrounds is briefly sketched as an application.
