Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime. (arXiv:2006.11263v3 [gr-qc] UPDATED)

Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime. (arXiv:2006.11263v3 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Miller_J/0/1/0/all/0/1">Jeremy Miller</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Pound_A/0/1/0/all/0/1">Adam Pound</a>

Extreme-mass-ratio inspirals, in which a stellar-mass compact object spirals
into a supermassive black hole in a galactic core, are expected to be key
sources for LISA. Modelling these systems with sufficient accuracy for LISA
science requires going to second (or {em post-adiabatic}) order in
gravitational self-force theory. Here we present a practical two-timescale
framework for achieving this and generating post-adiabatic waveforms. The
framework comprises a set of frequency-domain field equations that apply on the
fast, orbital timescale, together with a set of ordinary differential equations
that determine the evolution on the slow, inspiral timescale. Our analysis is
restricted to the special case of quasicircular orbits around a Schwarzschild
black hole, but its general structure carries over to the realistic case of
generic (inclined and eccentric) orbits in Kerr spacetime. In our restricted
context, we also develop a tool that will be useful in all cases: a formulation
of the frequency-domain field equations using hyperboloidal slicing, which
significantly improves the behavior of the sources near the boundaries. We give
special attention to the slow evolution of the central black hole, examining
its impact on both the two-timescale evolution and the earlier self-consistent
evolution scheme.

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