圆偏振真空pp波中的粒子运动
Particle motion in circularly polarized vacuum pp waves
AI总结：
本文研究含CPP波及Lukash波的一类圆偏振真空pp波中的粒子运动，利用其7参数共形对称性与Lukash-CPP变换，解析并数值发现Bianchi VI型下的有界测地线及粒子俘获。
摘要：
Bialynicki-Birula和Charzynski曾指出，双黑洞并合期间发射的引力波可以近似为一种圆偏振波，而这种波反过来可能俘获粒子[1]。本文研究一类引力波中的粒子运动，除圆偏振周期波（CPP）[2]外，该类引力波还包括Lukash为研究各向异性宇宙学模型而提出的波[3]。两种波都具有7参数共形对称性，除一般的5参数（破缺的）Carroll群外，该对称性还包含第6个等距。通过对时间进行共形重标度，Lukash时空可以变换为一个受扰CPP问题。当Lukash波为Bianchi VI型时，会出现有界测地线，这一结果通过解析和数值两种方式得到。它们的对称性也可以由Lukash-CPP关系导出。文中还讨论了粒子俘获。
英文摘要：
Bialynicki-Birula and Charzynski argued that a gravitational wave emitted during the merger of a black hole binary may be approximated by a circularly polarized wave which may in turn trap particles [1]. In this paper we consider particle motion in a class of gravitational waves which includes, besides circularly polarized periodic waves (CPP) [2], also the one proposed by Lukash [3] to study anisotropic cosmological models. Both waves have a 7-parameter conformal symmetry which contains, in addition to the generic 5-parameter (broken) Carroll group, also a 6th isometry. The Lukash spacetime can be transformed by a conformal rescaling of time to a perturbed CPP problem. Bounded geodesics, found both analytically and numerically, arise when the Lukash wave is of Bianchi type VI. Their symmetries can also be derived from the Lukash-CPP relation. Particle trapping is discussed.
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