Regularization parameters

This repository contains all the lastest regularization parameters. These parameters can be used to compute the regular field at the location of the particle. If you use these parameters, please cite the suitable references as laid out below as well as the BHPToolkit as outlined on the homepage. The most generic cases are listed first, with more specific cases following.

The notation used below follows that introduced by Heffernan et al. in Phys. Rev. D 82, 104023 (2012). This translates to the orignal notation as:
                                                A_a: F_a[-1],     B_a: F_a[0],     D_a: F_a[2],     F_a: F_a[4],     H_a: F_a[6].

We have made an effort to make this list and the digitally available parameters as extensive as possible, however if we have misrepresented any work or omitted any suitable research, please contact us via niels [dot] warburton [at] ucd [dot] ie.

Schwarzschild Spacetime

Geodesic self-force parameters

Field	Description	Parameters	Authors	Reference(s)
Scalar	Eccentric	Fa[-1], Fa[0]	L. Barack, A. Ori	Phys. Rev. D66 084022 (2002), arXiv:gr-qc/0204093
		Fa[2]	R. Hass, E. Poisson	Phys. Rev. D74 044009 (2006), arXiv:gr-qc/0605077
		Fa[4], Fa[6]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D82 104023 (2012), arXiv:1204.0794
	Circular	Fa[-1], Fa[0]	L. Barack, A. Ori	(1999)arXiv:gr-qc/9911040
		Fa[2]	S. Detweiler, E. Messaritaki, B.F. Whiting	Phys. Rev. D67 104016 (2003), arXiv:gr-qc/0205079
Electromagnetism	Eccentric	Fa[-1], Fa[0]	L. Barack, A. Ori	Phys. Rev. D67 024029 (2003), arXiv:gr-qc/0209072
		Fa[2]	R. Haas	arXiv:1112.3707
		Fa[4]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D82 104023 (2012), arXiv:1204.0794
Gravity	Eccentric	Fa[-1], Fa[0]	L. Barack, A. Ori	Phys. Rev. D67 024029 (2003), arXiv:gr-qc/0209072
		Fa[2], Fa[4]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D82 104023 (2012), arXiv:1204.0794

Useful scalar quantities for geodesic motion

Expression	Field	Description	Parameters	Authors	Reference(s)
Singular Field	Scalar	Eccentric	Φ[0], Φ[2], Φ[4], Φ[6]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D82 104023 (2012), arXiv:1204.0794
		Circular	Φ[0], Φ[2]	L.M. Diaz-Rivera, E. Messaritaki, B.F. Whiting, S. Detweiler	Phys. Rev. D70 124018 (2004), arXiv:gr-qc/0410011
Detweiler redshift	Gravity	Eccentric	H[0], H[2], H[4]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D82 104023 (2012), arXiv:1204.0794

Non-geodesic parameters

Expression	Field	Description	Parameters	Authors	Reference(s)
Self-force	Scalar	Eccentric	Fa[-1], Fa[0], Fa[2]	A. Heffernan A.Heffernan, A.C. Ottewill, N. Warburton, B. Wardell, P. Diener	arXiv:1403.6177 (2014) Class. Quant. Grav. 35 (2018) 19, 194001, arXiv:1712.01098
		Static	Fa[-1], Fa[0], Fa[2]	M. Casals, E. Poisson, I. Vega	Phys. Rev. D86 064033 (2012), arXiv:1206.3772
Singular Field	Scalar	Eccentric	Φ[0], Φ[2]	A.Heffernan, A.C. Ottewill, N. Warburton, B. Wardell, P. Diener	Class. Quant. Grav. 35 (2018) 19, 194001, arXiv:1712.01098

Kerr Spacetime

Geodesic self-force parameters

Field	Description	Parameters	Authors	Reference(s)
Scalar	Eccentric, inclined	Fa[-1], Fa[0]	L. Barack, A. Ori	Phys. Rev. Lett. 90:111101 (2003), arXiv:gr-qc/0212103
		Fa[2]	A. Heffernan	(2022) arxiv:2107.14750
	Eccentric, equatorial	Fa[2], Fa[4]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D89 024030 (2014), arXiv:1211.6446
Electromagnetism & gravity	Eccentric, inclined	Fa[-1], Fa[0]	L. Barack, A. Ori	Phys. Rev. Lett. 90:111101 (2003), arXiv:gr-qc/0212103
	Eccentric, equatorial	Fa[2]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D89 024030 (2014), arXiv:1211.6446

Useful scalar quantities for geodesic motion

Expression	Field	Description	Parameters	Authors	Reference(s)
Singular Field	Scalar	Eccentric, inclined	Φ[0], Φ[2]	A. Heffernan	(2022) arxiv:2107.14750
		Eccentric, equatorial	Φ[0], Φ[2], Φ[4]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D89 024030 (2014), arXiv:1211.6446
Detweiler redshift	Gravity	Eccentric, equatorial	H[0], H[2]	A. Heffernan, A. Ottewill, B. Wardell	Phys. Rev. D89 024030 (2014), arXiv:1211.6446