Gravitational Waveforms for Compact Binaries from Second-Order Self-Force Theory

We produce gravitational waveforms for nonspinning compact binaries undergoing a quasicircular inspiral. Our approach is based on a two-timescale expansion of the Einstein equations in second-order self-force theory, which allows first-principles waveform production in tens of milliseconds. Although the approach is designed for extreme mass ratios, our waveforms agree remarkably well with those from full numerical relativity, even for comparable-mass systems. Our results will be invaluable in accurately modeling extreme-mass-ratio inspirals for the LISA mission and intermediate-mass-ratio systems currently being observed by the LIGO-Virgo-KAGRA Collaboration.

Gravitational-Wave Energy Flux for Compact Binaries through Second Order in the Mass Ratio

Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field, and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modeling extreme-mass-ratio inspirals and will be useful in modeling intermediate-mass-ratio systems.

Self-Consistent Adiabatic Inspiral and Transition Motion

The transition motion of a point particle around the last stable orbit of Kerr is described at leading order in the transition-timescale expansion. Taking systematically into account all self-force effects, we prove that the transition motion is still described by the Painlevé transcendent equation of the first kind. Using an asymptotically matched expansions scheme, we consistently match the quasicircular adiabatic inspiral with the transition motion. The matching requires us to take into account the secular change of angular velocity due to radiation reaction during the adiabatic inspiral, which consistently leads to a leading-order radial self-force in the slow timescale expansion.

Learning about Black Hole Binaries from their Ringdown Spectra

The coalescence of two black holes generates gravitational waves that carry detailed information about the properties of those black holes and their binary configuration. The final coalescence cycles are in the form of a ringdown: a superposition of quasinormal modes of the merged remnant black hole. Each mode has an oscillation frequency and decay time that in general relativity is determined by the remnant's mass and spin. Measuring the frequency and decay time of multiple modes makes it possible to measure the remnant's mass and spin, and to test the waves against the predictions of gravity theories. In this Letter, we show that the relative amplitudes of these modes encode information about a binary's geometry. Focusing on the large mass-ratio limit, which provides a simple-to-use tool for effectively exploring parameter space, we demonstrate how a binary's geometry is encoded in the relative amplitudes of these modes, and how to parametrize the modes in this limit. Although more work is needed to assess how well this carries over to less extreme mass ratios, our results indicate that measuring multiple ringdown modes from coalescence may aid in measuring important source properties, such as the misalignment of its members' spins and orbit.