Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation

IF 26.3 2区 物理与天体物理 Q1 PHYSICS, PARTICLES & FIELDS
Timothy M. Adamo, Carlos Kozameh, Ezra T. Newman
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引用次数: 90

Abstract

A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues.

This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in an auxiliary four-complex dimensional space, \({\mathcal H}\)-space. They in turn play a dominant role in the applications.

The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi’s) integrals of the Weyl tensor, also at infinity.

More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum-conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

零测地线同余、渐近平坦时空及其物理解释
先验地,无剪切或渐近无剪切的零测地线同余没有什么特别之处。然而,令人惊讶的是,它们竟然拥有大量迷人的几何特性,并且在广义相对论的背景下,与各种物理上的重大效应密切相关。本文的目的就是试图全面展开这些问题。这项工作开始于对无剪切和渐近无剪切的零测地线同余理论的详细阐述,即与剪切的同余在未来保形零无穷处消失。本文的主要内容是对正则无剪切和渐近无剪切的零测地线同余空间的分析。这种分析导致复解析曲线的空间在一个辅助的四复维空间\({\mathcal H}\) -空间。它们反过来在应用程序中起主导作用。应用的中心是直接从渐近引力(和麦克斯韦)场本身提取渐近平坦时空的内部物理性质的问题,类似于在无穷远处通过麦克斯韦场上的积分来确定总电荷,或者通过Weyl张量的(邦迪)积分来确定内部质量(及其损失),也是在无穷远处。更具体地说,我们将看到渐近无剪切同余会使我们得到质心及其运动方程的渐近定义。这包括一个运动学意义,在质心运动方面,对于邦迪三动量。此外,我们还获得了对固有自旋和角动量的见解,包括具有定义良好的通量项的角动量守恒定律。当麦克斯韦场存在时,渐近无剪切同余允许我们确定/定义无限远处的电荷中心世界线和本征磁偶极矩。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Living Reviews in Relativity
Living Reviews in Relativity 物理-物理:粒子与场物理
CiteScore
69.90
自引率
0.70%
发文量
0
审稿时长
20 weeks
期刊介绍: Living Reviews in Relativity is a peer-reviewed, platinum open-access journal that publishes reviews of research across all areas of relativity. Directed towards the scientific community at or above the graduate-student level, articles are solicited from leading authorities and provide critical assessments of current research. They offer annotated insights into key literature and describe available resources, maintaining an up-to-date suite of high-quality reviews, thus embodying the "living" aspect of the journal's title. Serving as a valuable tool for the scientific community, Living Reviews in Relativity is often the first stop for researchers seeking information on current work in relativity. Written by experts, the reviews cite, explain, and assess the most relevant resources in a given field, evaluating existing work and suggesting areas for further research. Attracting readers from the entire relativity community, the journal is useful for graduate students conducting literature surveys, researchers seeking the latest results in unfamiliar fields, and lecturers in need of information and visual materials for presentations at all levels.
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