RESUMO
Scientific analysis for the gravitational wave detector LISA will require theoretical waveforms from extreme-mass-ratio inspirals (EMRIs) that extensively cover all possible orbital and spin configurations around astrophysical Kerr black holes. However, on-the-fly calculations of these waveforms have not yet overcome the high dimensionality of the parameter space. To confront this challenge, we present a user-ready EMRI waveform model for generic (eccentric and inclined) orbits in Kerr spacetime, using an analytical self-force approach. Our model accurately covers all EMRIs with arbitrary inclination and black hole spin, up to modest eccentricity (â²0.3) and separation (â³2-10 M from the last stable orbit). In that regime, our waveforms are accurate at the leading "adiabatic" order, and they approximately capture transient self-force resonances that significantly impact the gravitational wave phase. The model fills an urgent need for extensive waveforms in ongoing data-analysis studies, and its individual components will continue to be useful in future science-adequate waveforms.
RESUMO
For a self-gravitating particle of mass µ in orbit around a Kerr black hole of mass M â« µ, we compute the O(µ/M) shift in the frequency of the innermost stable circular equatorial orbit due to the conservative piece of the gravitational self-force acting on the particle. Our treatment is based on a Hamiltonian formulation of the dynamics in terms of geodesic motion in a certain locally defined effective smooth spacetime. We recover the same result using the so-called first law of binary black-hole mechanics. We give numerical results for the innermost stable circular equatorial orbit frequency shift as a function of the black hole's spin amplitude, and compare with predictions based on the post-Newtonian approximation and the effective one-body model. Our results provide an accurate strong-field benchmark for spin effects in the general-relativistic two-body problem.