Built on

V. Witzany, Hamilton-Jacobi equation for spinning particles near black holes, Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
A. Antonelli, M. van de Meent, A. Buonanno, J. Steinhoff, and J. Vines, Quasicircular inspirals and plunges from nonspinning effective-one-body Hamiltonians with gravitational self-force information, Phys. Rev. D 101
Original
1907
Earlier work this paper cites.
D. Bini and A. Geralico, New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: gyroscope precession, Phys. Rev. D 100
Original
1907
Earlier work this paper cites.
A. Pound, B. Wardell, N. Warburton, and J. Miller, Second-Order Self-Force Calculation of Gravitational Binding Energy in Compact Binaries, Phys. Rev. Lett. 124
Original
1908
Earlier work this paper cites.
D. Bini, T. Damour, and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123
Original
1909
Earlier work this paper cites.
S. Akcay, S. R. Dolan, C. Kavanagh, J. Moxon, N. Warburton, and B. Wardell, Dissipation in extreme-mass ratio binaries with a spinning secondary, Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
M. Mathisson, Neue mechanik materieller systemes, Acta Phys.Polon. 6
1937
Earlier work this paper cites.
A. Papapetrou, Spinning test-particles in general relativity. i, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 209
1951
Earlier work this paper cites.
T. Regge and J. A. Wheeler, Stability of a schwarzschild singularity, Physical Review 108
1957
Earlier work this paper cites.
W. G. Dixon, Dynamics of extended bodies in general relativity. i. momentum and angular momentum, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 314
1970
Earlier work this paper cites.
F. J. Zerilli, Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics, Physical Review D 2
1970
Earlier work this paper cites.
V. Moncrief, Gravitational perturbations of spherically symmetric systems. i. the exterior problem, Annals of Physics 88
1974
Earlier work this paper cites.
C. T. Cunningham, R. H. Price, V. Moncrief, C. T. Cunningham, R. H. Price, and V. Moncrief, Radiation from collapsing relativistic stars. ii. linearized even-parity radiation., ApJ 230
1979
Earlier work this paper cites.
K. S. Thorne and J. B. Hartle, Laws of motion and precession for black holes and other bodies, Phys. Rev. D 31
1985
Earlier work this paper cites.
A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59
1999
Earlier work this paper cites.
L. Barack and A. Ori, Mode sum regularization approach for the self-force in black hole spacetime, Physical Review D - Particles, Fields, Gravitation and Cosmology 61
1999
Earlier work this paper cites.
L. Barack, Y. Mino, H. Nakano, A. Ori, and M. Sasaki, Calculating the gravitational self force in schwarzschild spacetime, Physical Review Letters 88
2001
Earlier work this paper cites.
S. Detweiler and B. F. Whiting, Self-force via a green’s function decomposition, Physical Review D - Particles, Fields, Gravitation and Cosmology 67
2002
Earlier work this paper cites.
G. A. Piovano, A. Maselli, and P. Pani, Extreme mass ratio inspirals with spinning secondary: a detailed study of equatorial circular motion, Phys. Rev. D 102
Original
2004
Earlier work this paper cites.
K. Martel and E. Poisson, Gravitational perturbations of the schwarzschild spacetime: A practical covariant and gauge-invariant formalism, Phys. Rev. D 71
2005
Earlier work this paper cites.
J. Miller and A. Pound, Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime, Phys. Rev. D 103
Original
2006
Earlier work this paper cites.
S. Detweiler, A consequence of the gravitational self-force for circular orbits of the schwarzschild geometry, Physical Review D - Particles, Fields, Gravitation and Cosmology 77
2008
Earlier work this paper cites.

Similar

L. Barack, A. Ori, and N. Sago, Frequency-domain calculation of the self force: The High-frequency problem and its resolution, Phys. Rev. D 78
Original
2008
Cited alongside, same era.
T. Damour, Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism, Phys. Rev. D 81
Original
2010
Cited alongside, same era.
L. Barack, T. Damour, and N. Sago, Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism, Phys. Rev. D 82
Original
2010
Cited alongside, same era.
W.-B. Han, Gravitational Radiations from a Spinning Compact Object around a supermassive Kerr black hole in circular orbit, Phys. Rev. D 82
Original
2010
Cited alongside, same era.

Then

C. Kavanagh, D. Bini, T. Damour, S. Hopper, A. C. Ottewill, and B. Wardell, Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription, Phys. Rev. D 96
Original
2017
Later among the works it cites.
N. Warburton, T. Osburn, and C. R. Evans, Evolution of small-mass-ratio binaries with a spinning secondary, Phys. Rev. D 96
2017
Later among the works it cites.
A. Pound, Nonlinear gravitational self-force: second-order equation of motion, Phys. Rev. D 95
Original
2017
Later among the works it cites.
A. Heffernan, A. C. Ottewill, N. Warburton, B. Wardell, and P. Diener, Accelerated motion and the self-force in schwarzschild spacetime, Classical and Quantum Gravity 35
2017
Later among the works it cites.
D. Bini, T. Damour, A. Geralico, and C. Kavanagh, Detweiler’s redshift invariant for spinning particles along circular orbits on a Schwarzschild background, Phys. Rev. D 97

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2021

Self-Force Calculations with a Spinning Secondary

Mathews, Josh, Pound, Adam, Wardell, Barry

Understand

We compute the linear metric perturbation to a Schwarzschild black hole generated by a spinning compact object, specialising to circular equatorial orbits with an (anti-)aligned spin vector.

We derive a two-timescale expansion of the field equations, with an attendant waveform-generation framework, that includes all effects through first post-adiabatic order, and we use the Regge-Wheeler-Zerilli formalism in the frequency domain to generate waveforms that include the complete effect of the spin on the waveform phase.
We perform the calculations using expansions at fixed orbital frequency, increasing the computational efficiency and simplifying the procedure compared to previous approaches.
Finally, we provide the first fully relativistic, first-principles regularisation procedure for gauge invariant self-force quantities to linear order in spin.

Built on

V. Witzany, Hamilton-Jacobi equation for spinning particles near black holes, Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
A. Antonelli, M. van de Meent, A. Buonanno, J. Steinhoff, and J. Vines, Quasicircular inspirals and plunges from nonspinning effective-one-body Hamiltonians with gravitational self-force information, Phys. Rev. D 101
Original
1907
Earlier work this paper cites.
D. Bini and A. Geralico, New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: gyroscope precession, Phys. Rev. D 100
Original
1907
Earlier work this paper cites.
A. Pound, B. Wardell, N. Warburton, and J. Miller, Second-Order Self-Force Calculation of Gravitational Binding Energy in Compact Binaries, Phys. Rev. Lett. 124
Original
1908
Earlier work this paper cites.
D. Bini, T. Damour, and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123
Original
1909
Earlier work this paper cites.
S. Akcay, S. R. Dolan, C. Kavanagh, J. Moxon, N. Warburton, and B. Wardell, Dissipation in extreme-mass ratio binaries with a spinning secondary, Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
M. Mathisson, Neue mechanik materieller systemes, Acta Phys.Polon. 6
1937
Earlier work this paper cites.
A. Papapetrou, Spinning test-particles in general relativity. i, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 209
1951
Earlier work this paper cites.
T. Regge and J. A. Wheeler, Stability of a schwarzschild singularity, Physical Review 108
1957
Earlier work this paper cites.
W. G. Dixon, Dynamics of extended bodies in general relativity. i. momentum and angular momentum, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 314
1970
Earlier work this paper cites.
F. J. Zerilli, Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics, Physical Review D 2
1970
Earlier work this paper cites.
V. Moncrief, Gravitational perturbations of spherically symmetric systems. i. the exterior problem, Annals of Physics 88
1974
Earlier work this paper cites.
C. T. Cunningham, R. H. Price, V. Moncrief, C. T. Cunningham, R. H. Price, and V. Moncrief, Radiation from collapsing relativistic stars. ii. linearized even-parity radiation., ApJ 230
1979
Earlier work this paper cites.
K. S. Thorne and J. B. Hartle, Laws of motion and precession for black holes and other bodies, Phys. Rev. D 31
1985
Earlier work this paper cites.
A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59
1999
Earlier work this paper cites.
L. Barack and A. Ori, Mode sum regularization approach for the self-force in black hole spacetime, Physical Review D - Particles, Fields, Gravitation and Cosmology 61
1999
Earlier work this paper cites.
L. Barack, Y. Mino, H. Nakano, A. Ori, and M. Sasaki, Calculating the gravitational self force in schwarzschild spacetime, Physical Review Letters 88
2001
Earlier work this paper cites.
S. Detweiler and B. F. Whiting, Self-force via a green’s function decomposition, Physical Review D - Particles, Fields, Gravitation and Cosmology 67
2002
Earlier work this paper cites.
G. A. Piovano, A. Maselli, and P. Pani, Extreme mass ratio inspirals with spinning secondary: a detailed study of equatorial circular motion, Phys. Rev. D 102
Original
2004
Earlier work this paper cites.
K. Martel and E. Poisson, Gravitational perturbations of the schwarzschild spacetime: A practical covariant and gauge-invariant formalism, Phys. Rev. D 71
2005
Earlier work this paper cites.
J. Miller and A. Pound, Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime, Phys. Rev. D 103
Original
2006
Earlier work this paper cites.
S. Detweiler, A consequence of the gravitational self-force for circular orbits of the schwarzschild geometry, Physical Review D - Particles, Fields, Gravitation and Cosmology 77
2008
Earlier work this paper cites.

Similar

L. Barack, A. Ori, and N. Sago, Frequency-domain calculation of the self force: The High-frequency problem and its resolution, Phys. Rev. D 78
Original
2008
Cited alongside, same era.
T. Damour, Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism, Phys. Rev. D 81
Original
2010
Cited alongside, same era.
L. Barack, T. Damour, and N. Sago, Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism, Phys. Rev. D 82
Original
2010
Cited alongside, same era.
W.-B. Han, Gravitational Radiations from a Spinning Compact Object around a supermassive Kerr black hole in circular orbit, Phys. Rev. D 82
Original
2010
Cited alongside, same era.

Then

C. Kavanagh, D. Bini, T. Damour, S. Hopper, A. C. Ottewill, and B. Wardell, Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription, Phys. Rev. D 96
Original
2017
Later among the works it cites.
N. Warburton, T. Osburn, and C. R. Evans, Evolution of small-mass-ratio binaries with a spinning secondary, Phys. Rev. D 96
2017
Later among the works it cites.
A. Pound, Nonlinear gravitational self-force: second-order equation of motion, Phys. Rev. D 95
Original
2017
Later among the works it cites.
A. Heffernan, A. C. Ottewill, N. Warburton, B. Wardell, and P. Diener, Accelerated motion and the self-force in schwarzschild spacetime, Classical and Quantum Gravity 35
2017
Later among the works it cites.
D. Bini, T. Damour, A. Geralico, and C. Kavanagh, Detweiler’s redshift invariant for spinning particles along circular orbits on a Schwarzschild background, Phys. Rev. D 97

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

S. Hopper and C. R. Evans, Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a schwarzschild black hole, Phys. Rev. D 82

2010

Cited alongside, same era.

A. Pound, Self-consistent gravitational self-force, Phys. Rev. D 81