Automating the post-Newtonian expansion on a computer

Abstract

With several ground-based gravitational wave interferometers operating at design sensitivity the need for high-order post-Newtonian (PN) calculations of potentials waveforms etc. especially including spin effects has grown significantly over the last several years. Not only are these calculations necessary for precisely estimating the parameters of detected gravitational wave sources but they are also useful for providing more accurate models of binary evolutions in for example the effective one-body program and for computing the PN contributions to self-force effects in the extreme mass ratio limit. Since these calculations become more demanding to carry out at higher PN orders it is necessary to utilize symbolic computer algebra programs (such as Mathematica). Our aim is to automate PN calculations (of potentials power loss etc.) on the computer using the effective field theory (EFT) approach of Goldberger and Rothstein which is itself a systematic and algorithmic method for computing in the PN approximation. The EFT approach lends itself to automation through definite power counting rules that identify precisely those interactions appearing at a given PN order through Feynman rules and diagrams that provide an elegant way to side-step the need to explicitly solve the wave equation for metric perturbations (unlike in traditional methods) through working at the level of the action (a scalar) instead of equations of motion etc. We discuss our progress in automating these calculations on a computer using the EFT approach.