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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We develop the first model for extreme mass-ratio inspirals (EMRIs) with
misaligned angular momentum and primary spin, and zero eccentricity -- also
known as quasi-spherical inspirals -- evolving under the influence of the
first-order in mass ratio gravitational self-force. The forcing terms are
provided by an efficient spectral interpolation of the first-order
gravitational self-force in the outgoing radiation gauge. In order to speed up
the calculation of the inspiral we apply a near-identity (averaging)
transformation to eliminate all dependence of the orbital phases from the
equations of motion while maintaining all secular effects of the first-order
gravitational self-force at post-adiabatic order. The resulting solutions are
defined with respect to `Mino time' so we perform a second averaging
transformation so the inspiral is parametrized in terms of Boyer-Lindquist
time, which is more convenient of LISA data analysis. We also perform a similar
analysis using the two-timescale expansion and find that using either approach
yields self-forced inspirals that can be evolved to sub-radian accuracy in less
than a second. The dominant contribution to the inspiral phase comes from the
adiabatic contributions and so we further refine our self-force model using
information from gravitational wave flux calculations. The significant
dephasing we observe between the lower and higher accuracy models highlights
the importance of accurately capturing adiabatic contributions to the phase
evolution.
