Climbing up the memory staircase: Equatorial zoom-whirl orbits

TL;DR

This paper investigates the nonlinear gravitational memory effect in zoom-whirl orbits around Kerr black holes, analyzing mode contributions, evolution over time, and implications for detection with LISA.

Contribution

It provides a detailed analysis of the memory effect's staircase structure, mode contributions, and its evolution, including prospects for detection with LISA.

Findings

Memory effect exhibits a staircase pattern during zoom-whirl orbits.

Hereditary memory increases linearly with periapsis passages.

Potential detectability of the effect with LISA is discussed.

Abstract

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).