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共形无穷远

Conformal Infinity.

作者信息

Frauendiener Jörg

机构信息

Institut für Theoretische Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany.

出版信息

Living Rev Relativ. 2004;7(1):1. doi: 10.12942/lrr-2004-1. Epub 2004 Feb 2.

DOI:10.12942/lrr-2004-1
PMID:28179863
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5256109/
Abstract

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

摘要

共形无穷远的概念在爱因斯坦引力理论的研究中有着悠久的历史。如今，“共形无穷远”几乎与广义相对论研究的所有其他分支都相关，从量子化程序到抽象数学问题再到数值应用。这篇综述文章试图展示这个概念是如何从物理问题，即理解引力理论中的引力辐射和孤立系统的需求，逐渐且不可避免地演变而来的，以及它如何非常自然地适用于数值相对论中辐射问题的解决。引入了零无穷远的基本概念。介绍了弗里德里希的正则共形场方程，并讨论了它们的各种初值问题。最后，表明共形场方程在数值相对论中为研究诸如引力波传播和探测等全局问题提供了一种非常强大的方法。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/b3dffb661461/41114_2016_1_Fig17.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/b3dffb661461/41114_2016_1_Fig17.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/067fe38dd9a1/41114_2016_1_Fig1.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/639af18e1cf5/41114_2016_1_Fig8.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/ceb7513cee20/41114_2016_1_Fig9.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/c13a7966a0bb/41114_2016_1_Fig10.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/05c822b1ec35/41114_2016_1_Fig11.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/82fd4bfb2193/41114_2016_1_Fig12.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/d52f4e8c6ee7/41114_2016_1_Fig13.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/e5c828236019/41114_2016_1_Fig14.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/38a0c953d6db/41114_2016_1_Fig15.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/9dab81941316/41114_2016_1_Fig16.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a1cc/5256109/b3dffb661461/41114_2016_1_Fig17.jpg

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