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Hamilton-Jacobi equation for spinning particles near black holes
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Hamilton-Jacobi equation for spinning particles near black holes
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A compact stellar-mass object inspiralling onto a massive black hole deviates from geodesic motion due to radiation-reaction forces as well as finite-size effects. Such post-geodesic deviations need to be included with sufficient precision into wave-form models for the upcoming space-based gravitational-wave detector LISA. I present the formulation and solution of the Hamilton-Jacobi equation of geodesics near Kerr black holes perturbed by the so-called spin-curvature coupling, the leading order finite-size effect. In return, this solution allows to compute a number of observables such as the turning points of the orbits as well as the fundamental frequencies of motion. This result provides one of the necessary ingredients for waveform models for LISA and an important contribution useful for the relativistic two-body problem in general.
Forward citations
Cited by 14 Pith papers
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Quadrupolar tidal effects destroy the integrability of black hole geodesics: analytic proof and numerical evidence of chaos
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Symplectic mechanics of relativistic spinning compact bodies. III. quadratic-in-spin integrability in Type-D Einstein spacetimes: persistence and breakdown
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On the integrability of root-Kerr probe dynamics
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Extended 1PA self-force waveforms for slowly spinning primary and precessing secondary, with re-summed 1PAT1R variant showing improved accuracy against NR for q ≳ 5 and |χ1| ≲ 0.1.
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Classical eikonal in relativistic scattering
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Unexpected Symmetries of Kerr Black Hole Scattering
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