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The memory effect in gravitational wave (GW) signals is the phenomenon,wherein the relative position of two inertial GW detectors undergoes apermanent displacement owing to the passage of GWs through them. Measurement ofthe memory signal is an important target for future observations as itestablishes a connection between observations with field-theoretic results likethe soft-graviton theorems. Theoretically, the memory signal is predicted atthe leading order quadrupole formula for sources like binaries in hyperbolicorbits. This can be in the realm of observations by Advanced-LIGO,Einstein-Telescope, or LISA for stellar mass black-holes scattered by thesuper-massive black-hole at the galactic center. Apart from the direct memorycomponent there is a non-linear memory signal in the secondary GW emitted fromthe primary GW chirp-signals emitted by coalescing binaries. In this paper, wecompute the gravitational wave signals and their energy spectrum using thefield-theoretic method by computing the scattering amplitudes for eccentricelliptical and hyperbolic binary orbits. The field theoretic calculation givesus the gravitational waveforms of linear and non-linear memory signals directlyin the frequency space. The frequency domain templates are useful forextracting signals from the data. We compare our results with othercalculations of linear and non-linear memory signals in literature and pointout novel features we find in our calculations like the presence of$\log(\omega)$ terms in the linear memory from hyperbolic orbits.

Frequency space derivation of linear and non-linear memory gravitational wave signals from eccentric binary orbits