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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:
                                                Aa: Fa[-1],     Ba: Fa[0],     Da: Fa[2],     Fa: Fa[4],     Ha: Fa[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[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
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, 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

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Regularization parameters for Self-force calculations

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