关于黑洞周围扩展试验体动力学的可积性

IF 3.6 3区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
Paul Ramond
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引用次数: 0

摘要

在广义相对论中,扩展的测试体的运动受到其适当旋转或自旋的影响。我们提出了一个协变和物理自洽的哈密顿框架来研究这种运动,在身体的自旋中,包括自旋诱导的四极,在任意的背景时空中,高达二次阶。用哈密顿力学的自旋补充条件的选择和与局部洛伦兹不变性相关的简并进行了严格的处理。将这种形式应用于克尔度规所描述的背景时空,证明了任何测试致密物体围绕旋转黑洞的运动在物体自旋中定义了一个线性有序的可积哈密顿系统。此外,当致密物体具有孤立黑洞所期望的可变形性时,这种可积性在自旋的二次阶上仍然成立。通过利用黑洞双星中独特的对称性,我们的分析结果澄清了长期以来关于非对称紧致双星运动中自旋引起的混沌的数值猜想,并可能为改进当前的引力波形建模提供一个强大的框架。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the integrability of extended test body dynamics around black holes
In general relativity, the motion of an extended test body is influenced by its proper rotation, or spin. We present a covariant and physically self-consistent Hamiltonian framework to study this motion, up to quadratic order in the body’s spin, including a spin-induced quadrupole, and in an arbitrary background spacetime. The choice of spin supplementary condition and degeneracies associated with local Lorentz invariance are treated rigorously with adapted tools from Hamiltonian mechanics. Applying the formalism to a background space-time described by the Kerr metric, we prove that the motion of any test compact object around a rotating black hole defines an integrable Hamiltonian system to linear order in the body’s spin. Moreover, this integrability still holds at quadratic order in spin when the compact object has the deformability expected for an isolated black hole. By exploiting the unique symmetries at play in black hole binaries, our analytical results clarify longstanding numerical conjectures regarding spin-induced chaos in the motion of asymmetric compact binaries, and may provide a powerful framework to improve current gravitational waveform modelling.
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来源期刊
Classical and Quantum Gravity
Classical and Quantum Gravity 物理-天文与天体物理
CiteScore
7.00
自引率
8.60%
发文量
301
审稿时长
2-4 weeks
期刊介绍: Classical and Quantum Gravity is an established journal for physicists, mathematicians and cosmologists in the fields of gravitation and the theory of spacetime. The journal is now the acknowledged world leader in classical relativity and all areas of quantum gravity.
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