arXiv 2409.042812024-09-10gr-qc

超越线性近似：来自 Brill 与 Teukolsky 初始数据集的 Arnowitt-Deser-Misner 质量的相似性

Similarity in the Arnowitt-Deser-Misner Mass from Brill and Teukolsky Initial Data Sets Beyond the Linear Approximation

R. F. Aranha, H. P. de Oliveira

AI总结：

该研究比较 Brill 与 Teukolsky 轴对称引力波初始数据，发现尽管二者线性结构不同，其 ADM 质量随初始振幅的分布均呈现长程相互作用系统中常见的非广延关系。

摘要：

真空轴对称时空最常见的两类初始数据是 Brill 引力波和 Teukolsky 引力波。这些数据随后的数值演化表现出不同性质，主要与临界引力坍缩有关。理解这些差异的一种可能途径是首先考察线性层面：Brill 波具有多极结构，而 Teukolsky 波具有四极结构。尽管二者在线性和非线性层面结构不同，我们表明这些引力波初始数据具有一种出乎意料的相似性，涉及 ADM 质量作为初始波振幅函数的分布。更具体地说，两种构型都满足一种非广延关系，这种关系常见于由长程相互作用支配的系统。

英文摘要：

The two most common initial data for vacuum axisymmetric spacetimes are the Brill and Teukolsky gravitational waves. The subsequent numerical evolution of these data exhibits distinct properties mainly associated with the critical gravitational collapse. A possible way of understanding these differences is first to look at the linear level, where the Brill waves have a multipolar structure, while the Teukolsky waves have a quadrupolar structure. Despite being structurally distinct at the linear and nonlinear levels, we show that these gravitational wave initial data share an unexpected similarity related to the distribution of ADM mass as a function of the initial wave's amplitude. More specifically, both configurations satisfy a nonextensive relation, commonly seen in systems governed by long range interactions.

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