The nonlinear, or null gravitational memory effect for zoom-whirl orbits around fast spinning Kerr black holes for extreme mass ratio systems has a staircase structure. The latter is characterized by a periodic fast increase in the memory during the whirl phases of the orbit, and near constant levels when the orbit is near apoapsis. We study the contribution of different spherical harmonic modes to this effect, and discuss the relative importance thereof. Because the hereditary memory effect increases in magnitude linearly in the number of periapsis passages on a dynamical time scale, while the oscillatory parent gravitational waves are sourced by an orbit that evolves on a much longer radiation reaction time scale, the magnitude of the former relative to the latter increases with time. We also consider orphan memory and the memory effect for extreme mass ratio inspirals. We then discuss the prospect of detection with the Laser Interferometer Space Antenna (LISA).

中文翻译：

---

攀登记忆阶梯：赤道缩放-旋转轨道

极端质量比系统的快速旋转的Kerr黑洞周围的缩放旋涡轨道的非线性或零重力记忆效应具有阶梯结构。后者的特征在于在轨道的旋涡阶段期间记忆的周期性快速增加，并且在轨道接近顶峰时接近恒定的水平。我们研究了不同球形谐波模式对此效应的贡献，并讨论了其相对重要性。由于遗传记忆效应的大小在动态时间尺度上的围攻通道数目呈线性增加，而振荡的母体引力波是由在更长的辐射反应时间尺度上演化的轨道产生的，因此前者的幅度相对于后者随时间增加。我们还考虑了孤儿记忆和极端质量比率吸气的记忆效应。然后，我们讨论使用激光干涉仪空间天线（LISA）进行检测的前景。