The mode-sum regularization approach to self-force calculations relies on using an analytically computed approximation to the Detweiler-Whiting singular field to derive so-called mode-sum regularization parameters. On this page, I will provide a collection of codes and Mathematica scripts which are useful for mode-sum regularization calculations.

Singular field of a point particle

The derivation of regularization parameters requires expansions of the singular field in the distance from the world-line. These expansions involve expressions which are too long to be included in a paper. Instead, we give them here as Mathematica code. For a full description of how these are calculated, see Phys. Rev. D 82, 104023 (2012).

For each case, we give a bzipped Mathematica package file containing the definition of a symbol of the same name. Tensors of rank n are given as n-dimensional lists, the elements of which correspond to the t, r, w1 and w2 components of the tensor. Each element is a SeriesData object in powers of ε, starting at order 1/ε. For example, to obtain the order 1/ε contribution to the t,t component of the singular metric perturbation:

Import["hS.m.bz2"];
Coefficient[hS[[1, 1]], \[Epsilon], -1]

The following expressions are available:

• hS.m.bz2: Singular metric perturbation for a generic geodesic in Schwarzschild spacetime written in Riemann normal coordinates to order ε^4.

Regularization parameters for Schwarzschild spacetime

High order regularization parameters for the Schwarzschild spacetime were derived in Phys. Rev. D 82, 104023 (2012). for the case of a generic geodesic orbit. The expressions are given in Section V of the paper. However, as they are quite long, we are providing them here in a more convenient electronic form as a Mathematica notebook. We also include regularization parameters for other cases not explicitly given in the paper.

Regularization parameters for Kerr spacetime

High order regularization parameters for the Kerr spacetime were derived in Phys. Rev. D 89, 024030 (2014) for the case of a generic equatorial geodesic orbit. Some expressions are given in the paper. However, as they are quite long, we are providing them here in a more convenient electronic form as a Mathematica notebook. We also include regularization parameters for other cases not explicitly given in the paper.