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arXiv 0906.0968gr-qc
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任意质量比和相对速度双星引力辐射和反应的新分析方法

New analytical methods for gravitational radiation and reaction in binaries with arbitrary mass ratio and relative velocity

Chad R. Galley, Bei-Lok Hu

摘要:

本文提出了一个新的分析框架来描述质量不等的引力双星系统以任意相对速度运动的动力学,考虑了来自两个致密天体的以潮汐形变、引力波和自力形式的反作用.允许所有的动力学变量以自洽的方式相互作用,这种形式确保了所有涉及的动力学量在背景时空中是守恒的,并且在保持背景几何的一般坐标变换下服从规范不变性。因为它是基于一个广义微扰理论和重要的新的重点是对所有的动力学变量的自洽性,我们称之为自洽反作用引力微扰理论(GP-SCB)。为了说明这种形式主义是如何实现的,我们微扰地构造了一组自洽的运动方程的吸气引力双星,它不需要额外的假设,如慢运动,弱场或小质量比的制定。这种情况应该包括具有其他一般参数(例如,在第二部分中,我们讨论了如何将质量比作为后牛顿有效场论(PN-EFT)方法中的微扰参数,从而将Goldberger和Rothstein关于等质量双星的工作推广到变质量双星。我们提供了粗略的估计较高的后牛顿的订单需要确定的引力波周期的数量,以指定的精度,落入探测器的带宽。

英文摘要:

We present a new analytical framework for describing the dynamics of a gravitational binary system with unequal masses moving with arbitrary relative velocity, taking into account the backreaction from both compact objects in the form of tidal deformation, gravitational waves and self forces. Allowing all dynamical variables to interact with each other in a self-consistent manner this formalism ensures that all the dynamical quantities involved are conserved on the background spacetime and obey the gauge invariance under general coordinate transformations that preserve the background geometry. Because it is based on a generalized perturbation theory and the important new emphasis is on the self-consistency of all the dynamical variables involved we call it a gravitational perturbation theory with self-consistent backreaction (GP-SCB). As an illustration of how this formalism is implemented we construct perturbatively a self-consistent set of equations of motion for an inspiraling gravitational binary, which does not require extra assumptions such as slow motion, weak-field or small mass ratio for its formulation. This case should encompass the inspiral and possibly the plunge and merger phases of binaries with otherwise general parameters (e.g., mass ratio and relative velocity) though more investigation is needed to substantiate it. In the second part, we discuss how the mass ratio can be treated as a perturbation parameter in the post-Newtonian effective field theory (PN-EFT) approach, thus extending the work of Goldberger and Rothstein for equal mass binaries to variable mass ratios. We provide rough estimates for the higher post-Newtonian orders needed to determine the number of gravitational wave cycles, with a specified precision, that fall into a detector's bandwidth.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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