New structures in gravitational radiation
New structures in gravitational radiation
复制标题
DOI：
10.4310/atmp.2022.v26.n3.a1
复制
发表时间：
2020-10
影响因子：
1.5
通讯作者：
L. Bieri
中科院分区：
文献类型：
--
作者：
L. Bieri
我们研究了描述中微子辐射的爱因斯坦真空方程和爱因斯坦零流体方程。我们在引力波和缓慢衰变的渐近平坦时空的记忆中发现了新的结构。众所周知，对于更强的数据衰减，包括数据在紧致集之外是稳定的，引力波记忆是有限的，并且只有电奇偶。在这篇文章中，我们研究在粗略意义上渐近平坦的一般时空。也就是说，数据向Minkowski空间向无穷远处的衰减非常缓慢。作为一个主要的新特征，我们证明了在爱因斯坦真空中存在由曲率张量的磁性部分(A)和(B)在爱因斯坦零流体方程中产生的发散磁记忆。磁记忆在纯重力的爱因斯坦真空环境(A)中自然发生。在情况(B)中，在最终的解类别中，磁记忆还包含来自中微子的能量动量张量的卷曲项，该张量也以上述速率发散。电记忆也是发散的，它是由曲率张量的电部分产生的，在爱因斯坦零流体情况下也是由相应的能量动量分量产生的。此外，我们在这些流形中发现了更精细的结构的全景。其中一些表现为对电记忆和磁记忆的额外贡献。我们的定理适用于与爱因斯坦方程耦合的任何类型的物质或能量，只要数据缓慢衰减到无穷大，并且满足其他条件。新的结果有着广泛的应用范围，从数学广义相对论到引力波天体物理学，探测暗物质和其他物理学课题。
We investigate the Einstein vacuum equations as well as the Einstein-null fluid equations describing neutrino radiation. We find new structures in gravitational waves and memory for asymptotically-flat spacetimes of slow decay. It has been known that for stronger decay of the data, including data being stationary outside a compact set, gravitational wave memory is finite and of electric parity only. In this article, we investigate general spacetimes that are asymptotically flat in a rough sense. That is, the decay of the data to Minkowski space towards infinity is very slow. As a main new feature, we prove that there exists diverging magnetic memory sourced by the magnetic part of the curvature tensor (a) in the Einstein vacuum and (b) in the Einstein-null-fluid equations. The magnetic memory occurs naturally in the Einstein vacuum setting (a) of pure gravity. In case (b), in the ultimate class of solutions, the magnetic memory contains also a curl term from the energy-momentum tensor for neutrinos also diverging at the aforementioned rate. The electric memory diverges too, it is generated by the electric part of the curvature tensor and in the Einstein-null-fluid situation also by the corresponding energy-momentum component. In addition, we find a panorama of finer structures in these manifolds. Some of these manifest themselves as additional contributions to both electric and magnetic memory. Our theorems hold for any type of matter or energy coupled to the Einstein equations as long as the data decays slowly towards infinity and other conditions are satisfied. The new results have a multitude of applications ranging from mathematical general relativity to gravitational wave astrophysics, detecting dark matter and other topics in physics.