arXiv 2105.091662021-05gr-qchep-th

宇宙学常数为零时的渐近结构

Asymptotic Structure with vanishing cosmological constant

Francisco Fernández-Álvarez, José M. M. Senovilla

备注：: 45 pages, first of two papers, minor corrections, accepted version for publication
发表信息：: Class. Quant. Grav. 39 165011 2022
DOI：: 10.1088/1361-6382/ac387e

摘要：

这是第一个两篇论文致力于渐近结构的时空中存在一个非负的宇宙学常数$Λ$。这第一篇论文关注的是$Λ=0$的案例。我们的方法是完全基于潮汐性质的引力场，因此，在“潮汐能”建立与外尔曲率。特别是，我们使用的（辐射）渐近supermomenta计算从重新缩放的外尔张量在无穷远提供一个新的表征辐射逃逸，或进入，时空。我们的新标准是很容易实现的，是完全等价的经典的新闻张量的基础上。它的优点之一是，它的配方可以很容易地适应的情况下，$Λ>0$涵盖在第二篇论文。我们推导出一般的能量动量损失公式，包括物质项和所有与选择任意叶理和超平移有关的因素。我们还重新审视，并提出了一个完整的重新制定的传统剥离行为与整洁的几何结构，导致，特别是根据辐射准则的supermomenta的渐近对齐。

英文摘要：

This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $Λ$. This first paper is concerned with the case of $Λ=0$. Our approach is fully based on the tidal nature of the gravitational field and therefore on the `tidal energies' built with the Weyl curvature. In particular, we use the (radiant) asymptotic supermomenta computed from the rescaled Weyl tensor at infinity to provide a novel characterisation of radiation escaping from, or entering into, the space-time. Our new criterion is easy to implement and shown to be fully equivalent to the classical one based on the news tensor. One of its virtues is that its formulation can be easily adapted to the case with $Λ>0$ covered in the second paper. We derive the general energy-momentum-loss formulae including the matter terms and all factors associated to the choices of arbitrary foliation and of super-translation. We also revisit and present a full reformulation of the traditional peeling behaviour with a neat geometrical construction that leads, in particular, to an asymptotic alignment of the supermomenta in accordance with the radiation criterion.

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英文摘要：

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