Asymptotic behavior of massless fields and the memory effect
Asymptotic behavior of massless fields and the memory effect
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DOI：
10.1103/physrevd.99.084007
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发表时间：
2019-01
影响因子：
5
通讯作者：
Gautam Satishchandran;R. Wald
中科院分区：
文献类型：
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作者：
Gautam Satishchandran;R. Wald
我们研究了无质量标量，电磁和线性化引力扰动的行为在零无穷大附近的d \geq 4维闵可夫斯基时空（偶数和奇数维）的假设下，这些领域承认一个适当的扩展1/r。我们还研究了在所有维度d\geq 4中零无穷大附近渐近平坦的非线性引力扰动的行为。然后，我们考虑在完全非线性广义相对论的记忆效应。我们表明，在偶数维，记忆效应首先出现在库仑秩序-即，order 1/r^{d-3}--并且可以自然地分解为“空内存”和“普通内存”。记忆与一个能量流到零无穷大有关。我们表明，普通的内存与度量未能在一个顺序更快的下降比库仑在过去和/或未来是固定的。在奇数维，我们表明，总的记忆效应在库仑秩序和较慢的下降总是消失。可编程存储器总是“标量类型”，但普通存储器可以是任何类型（即，标量、向量或张量）类型。在4维时空中，我们给出了一个线性引力的明确例子，它产生了一个非平凡向量（即，磁宇称）1/r级的普通记忆效应。我们表明，标量存储器是由一个单同态描述，向量和张量存储器不能。在d=4维，我们表明，有一个密切的关系之间的记忆和与超平移的电荷和通量的表达式。我们分析的解决方案，是固定在库仑秩序的行为，并显示这些建议“对映匹配”之间的未来和过去的零无限，从而产生守恒定律。本文分析了量子引力中“外”态的记忆发散和红外发散之间的关系，并解释了“软定理”的本质。
We investigate the behavior of massless scalar, electromagnetic, and linearized gravitational perturbations near null infinity in d \geq 4 dimensional Minkowski spacetime (of both even and odd dimension) under the assumption that these fields admit a suitable expansion in 1/r. We also investigate the behavior of asymptotically flat, nonlinear gravitational perturbations near null infinity in all dimensions d\geq 4. We then consider the memory effect in fully nonlinear general relativity. We show that in even dimensions, the memory effect first arises at Coulombic order--i.e., order 1/r^{d-3}--and can naturally be decomposed into `null memory' and `ordinary memory.' Null memory is associated with an energy flux to null infinity. We show that ordinary memory is associated with the metric failing to be stationary at one order faster fall-off than Coulombic in the past and/or future. In odd dimensions, we show that the total memory effect at Coulombic order and slower fall-off always vanishes. Null memory is always of `scalar type', but the ordinary memory can be of any (i.e., scalar, vector, or tensor) type. In 4-spacetime dimensions, we give an explicit example in linearized gravity which gives rise to a nontrivial vector (i.e., magnetic parity) ordinary memory effect at order 1/r. We show that scalar memory is described by a diffeomorphism; vector and tensor memory cannot be. In d=4 dimensions, we show that there is a close relationship between memory and the charge and flux expressions associated with supertranslations. We analyze the behavior of solutions that are stationary at Coulombic order and show how these suggest `antipodal matching' between future and past null infinity, which gives rise to conservation laws. The relationship between memory and infrared divergences of the `out' state in quantum gravity is analyzed, and the nature of the `soft theorems' is explained.