We revisit the issue of memory effects, i.e. effects giving rise to a net cumulative change of the configuration of test particles, using a toy model describing the emission of radiation by a compact source and focusing on the scalar, hence non-radiative, part of the Riemann curvature. Motivated by the well known fact that gravitational radiation is accompanied by a memory effect, i.e. a permanent displacement of the relative separation of test particles, present after radiation has passed, we investigate the existence of an analog effect in the non-radiative part of the gravitational field. While quadrupole and higher multipoles undergo oscillations responsible for gravitational radiation, energy, momentum and angular momentum are conserved charges undergoing non-oscillatory change due to radiation emission. We show how the source re-arrangement due to radiation emission produce time-dependent scalar potentials which induce a time variation in the scalar part of the Riemann curvature tensor. As a result, on general grounds a velocity memory effect appears, depending on the inverse of the square of the distance of the observer from the source, thus making it almost impossible to observe, as shown by comparison to the planned gravitational detector noise spectral densities.

我们使用一个描述紧凑源辐射发射的玩具模型，并关注标量（即非辐射部分）的玩具模型，重新研究了记忆效应的问题，即引起测试粒子构型的净累积变化的效应。黎曼曲率。受众所周知的事实的影响，重力辐射伴随着记忆效应，即在辐射通过后存在的测试粒子相对分离的永久位移，我们研究了非辐射中类似效应的存在引力场的一部分。尽管四极及更高的多极经历负责重力辐射的振荡，但能量，动量和角动量是守恒电荷，由于辐射发射而发生了非振荡性变化。我们展示了由于辐射发射而引起的源重排如何产生与时间有关的标量电势，该标量电势在黎曼曲率张量的标量部分中引起时间变化。结果，在一般情况下，会出现速度记忆效应，这取决于观察者到源的距离的平方的倒数，因此几乎不可能观察到，如通过与计划的重力探测器噪声频谱密度进行比较所显示的那样。