标题： 引力辐射中的新结构 显示英文标题

标题： New Structures in Gravitational Radiation

摘要： 我们研究爱因斯坦真空方程以及描述中微子辐射的爱因斯坦-零流体方程。 我们在渐近平坦时空的慢衰减情况下发现了引力波和记忆的新结构。 这些结构不会出现在数据在紧致集之外为稳态的时空中出现。 相反，更一般的情况下表现出更丰富的几何分析相互作用，展示了这些更一般系统的物理特性。 已知对于数据更强衰减的情况，引力波记忆是有限的且仅具有电偶极子性质。 我们研究的是在粗略意义上渐近平坦的时空，其中数据向无限远处衰减到闵可夫斯基空间非常缓慢。 主要新特征：我们证明存在由曲率张量的磁部分（a）在爱因斯坦真空和（b）在爱因斯坦-零流体方程中产生的发散磁记忆。 磁记忆自然出现在爱因斯坦真空设置（a）纯引力的情况下。 在情况（b）中，在最终类解中，磁记忆还包含来自中微子能量动量张量的旋度项，该旋度项也以最高速率发散。 电记忆也会发散，它由曲率张量的电部分产生，并且在爱因斯坦-零流体情况下也由相应的能量动量分量产生。 此外，我们在这些流形中发现了一系列更精细的结构。 其中一些表现为对电记忆和磁记忆的额外贡献。 我们的定理适用于任何类型的物质或能量耦合到爱因斯坦方程的情况，只要数据向无限远处缓慢衰减并且满足其他条件。 新结果有许多应用，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主题。 显示英文摘要

摘要： 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. These structures do not arise in spacetimes resulting from data that is stationary outside a compact set. Rather the more general situations exhibit richer geometric-analytic interactions displaying the physics of these more general systems. It has been known that for stronger decay of the data gravitational wave memory is finite and of electric parity only. We investigate general spacetimes that are asymptotically flat in a rough sense, where the decay of the data to Minkowski space towards infinity is very slow. 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 also contains a curl term from the energy-momentum tensor for neutrinos also diverging at the highest 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 many applications ranging from mathematical general relativity to gravitational wave astrophysics, detecting dark matter and other topics in physics.