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The time evolution of an EMRI (extreme mass ratio inspiral) is
prolonged and contains many number of cycles. In order to detect the
gravitational waves (GW) signal from these systems, it is important to
model the waveform accurately. Typically, we use two timescale
approximation, where the slow timescale describes the inspiral of the
binary, and the fast timescale characterises its orbital motions. In this
talk, I will consider a system composed of a charged particle moving in
the background of a magnetised Kerr black hole, which serves as an
analogue to EMRI system. I will introduce the instantaneous
electromagnetic self force to describe the time evolution of this system
and model the resonance crossing. In the beginning of the talk, I will
give a brief introduction to these resonances, while primarily focus on
the prolonged resonance in our case. In this resonance, the integrability
of the Hamiltonian is broken and we encounter chaos under certain
conditions. Another key objective of this talk is to compare the results
between instantaneous self force and approximated adiabatic treatment.
Finally, I will attempt to point out the possible implications of these
results in the gravitational sector. |