  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).

General Relativity and Quantum Cosmology