The effective source approach to self-force calculations relies on an analytically computed approximation to the Detweiler-Whiting singular field. These approximations are typically implemented as series expansions in the distance of the field point from the point particle. On this page, I will provide a collection of codes and Mathematica scripts for computing these expansions.

Scalar self-force

Circular orbits in Kerr spacetime

The effective source approach was first applied to orbits in Kerr spacetime in Phys. Rev. D 84, 084001 (2011), which considered the case of an equatorial, circular geodesic orbit. This made use of an approximation to the singular field which is accurate to fourth order. The expressions for this are given in Appendix A of the paper. However, as they are quite long, I am providing them in a more convenient electronic form as a Mathematica notebook.

Generic orbits in Schwarzschild and Kerr spacetimes

The paper Phys. Rev. D 85, 104044 (2012) gives a detailed description of the effective source approach, and derives expressions for the effective source for generic orbits in Schwarzschild and Kerr spacetime. As most of the expressions were too long to be included in the paper, we provide them instead as a Mathematica notebook. We have also developed a C code which may be used as a black box for computing the effective source.

Gravitational self-force

Circular orbits in Schwarzschild spacetime (frequency-domain)

The effective source approach was first applied to compute the gravitational self-force in the frequency-domain in arXiv:1505.07841, which considered the case of an circular geodesic orbit in Schwarzschild spacetime. This made use of an effective source derived from spherical-harmonic mode puncture functions. The expressions for these puncture functions are given in Appendix C of the paper. However, as they are quite long, I am providing them in a more convenient electronic form as a Mathematica notebook, along with the higher-order versions referred to in the paper.