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For a Schwarzchild black hole of mass $M$, we consider a test particle falling from rest at infinity and becoming trapped, at late time, on the unstable circular orbit of radius $r=4GM/c^2$.
Ein invarianter Variationssatz für die Bewegung mehrerer elektrischer Massenteilchen
Adriann Daniel Fokker · 1929
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Classical electrodynamics in terms of direct interparticle action
John Archibald Wheeler and Richard Phillips Feynman · 1949
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Conservation Theorems in Modified Electrodynamics
J. W. Dettman and A. Schild · 1954
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Electromagnetic Two-Body Problem
Alfred Schild · 1963
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Gravitational field of a particle falling in a Schwarzschild geometry analyzed in tensor harmonics
Frank J. Zerilli · 1970
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Stability of gravity with a cosmological constant
L.F. Abbott and S. Deser · 1982
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Testing gravity to second postNewtonian order: A Field theory approach
Thibault Damour and Gilles Esposito-Farese · 1996
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Effective one-body approach to general relativistic two-body dynamics
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Transition from inspiral to plunge in binary black hole coalescences
Alessandra Buonanno and Thibault Damour · 2000
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Mode sum regularization approach for the selfforce in black hole space-time
Leor Barack and Amos Ori · 2000
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Gravitational selfforce and gauge transformations
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Leor Barack · 2001
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Gravitational self-force and gauge transformations
Leor Barack and Amos Ori · 2001
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Computing the gravitational selfforce on a compact object plunging into a Schwarzschild black hole
Leor Barack and Carlos O. Lousto · 2002
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Calculating the gravitational selfforce in Schwarzschild space-time
Leor Barack, Yasushi Mino, Hiroyuki Nakano, Amos Ori, and Misao Sasaki · 2002
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Low multipole contributions to the gravitational self-force
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Harmonic-gauge dipole metric perturbations for weak-field circular orbits in Schwarzschild spacetime
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Perturbations of Schwarzschild black holes in the lorenz gauge: Formulation and numerical implementation
Leor Barack and Carlos O. Lousto · 2005
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Gravitational self-force on a particle in circular orbit around a Schwarzschild black hole
Leor Barack and Norichika Sago · 2007
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Harmonic gauge perturbations of the Schwarzschild metric
Mark V. Berndtson · 2007
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Tobias S. Keidl, John L. Friedman, and Alan G. Wiseman · 2007
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Thibault Damour and Alessandro Nagar · 2009
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Thibault Damour · 2010
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Maarten van de Meent · 2017
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(unpublished thesis, Southampton 2017)
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Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order
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