作为相对论系统的极端黑洞与开普勒动力学

IF 0.8 4区 数学 Q3 MATHEMATICS, APPLIED
Dijs de Neeling, Diederik Roest, Marcello Seri, Holger Waalkens
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引用次数: 0

摘要

最近探测到的来自吸积黑洞双星的引力波重新引发了人们对相对论双体系统动力学的兴趣。后者的保守部分是由黑洞双星广义相对论描述的所谓后牛顿展开得到的哈密顿系统给出的。在本文中,我们研究了是否存在具有椭圆轨道的类似开普勒动力学的相对论双星这一一般性问题。我们证明,对于具有类似开普勒形式哈密顿的相对论系统,确实存在与开普勒问题等价的轨道。这种形式是由带有电荷和标量发的极端黑洞实现的,在任意质量比的后牛顿展开中至少达到一阶,在双星的测试质量极限的后牛顿展开中达到所有阶。此外,在牛顿后五阶,我们证明了类似开普勒形式的哈密顿可以通过典范变换和时间重参数化与开普勒问题明确相关,而且所有守恒拉普拉斯-伦格-伦兹类矢量的哈密顿都以这种方式与开普勒相关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Extremal Black Holes as Relativistic Systems with Kepler Dynamics

The recent detection of gravitational waves emanating from inspiralling black hole binaries has triggered a renewed interest in the dynamics of relativistic two-body systems. The conservative part of the latter are given by Hamiltonian systems obtained from so-called post-Newtonian expansions of the general relativistic description of black hole binaries. In this paper we study the general question of whether there exist relativistic binaries that display Kepler-like dynamics with elliptical orbits. We show that an orbital equivalence to the Kepler problem indeed exists for relativistic systems with a Hamiltonian of a Kepler-like form. This form is realised by extremal black holes with electric charge and scalar hair to at least first order in the post-Newtonian expansion for arbitrary mass ratios and to all orders in the post-Newtonian expansion in the test-mass limit of the binary. Moreover, to fifth post-Newtonian order, we show that Hamiltonians of the Kepler-like form can be related explicitly through a canonical transformation and time reparametrisation to the Kepler problem, and that all Hamiltonians conserving a Laplace – Runge – Lenz-like vector are related in this way to Kepler.

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来源期刊
CiteScore
2.50
自引率
7.10%
发文量
35
审稿时长
>12 weeks
期刊介绍: Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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