Talk at Perimeter Institute

PI-talkOn Tuesday, March 24 2015 I gave a talk at Perimeter Institute in Waterloo, Canada. In the presentation, I described xAct, a tensor algebra package for Mathematica which was primarily developed by Jose Maria Martin-Garcia. The talk is available online through the Perimeter Institute video library and the Mathematica notebook containing the slides from the talk are available for download separately.

Analytical high-order post-Newtonian expansions for extreme mass ratio binaries

The preprint of my latest paper with Chris Kavanagh and Adrian Ottewill is now available on the arXiv. The abstract for the article is below:

We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values of  \ell, and in doing so develop an efficient new method for generating the MST renormalised angular momentum,  \nu.

Update: The paper has now been published as Phys. Rev. D 92, 084025 (2015).

Self-force: Computational Strategies

I have recently finished a review paper which is due to be published by Springer in Fundamental Theories of Physics Vol. 179, as part of the book Equations of Motion in Relativistic Gravity. A preprint of the article is available on the arXiv. The abstract for the article is below:

Building on substantial foundational progress in understanding the effect of a small body’s self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) mode-sum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.

Installing GRTensor on Mac OSX

GRTensor is a very handy Maple package for doing calculations in General Relativity. Given a specific metric, it’s great at calculating the components of tensors. You can define your own tensors or use the predefined ones. You can even define your own metrics.

The install instructions in the Readme file are fairly good if you’re a Windows or Linux user. As is often the case, however, there are one or two catches when installing on Mac OS X. With that in mind, the following instructions should help with the installation:

Continue reading Installing GRTensor on Mac OSX

GRTensor: Metrics and Mac OS X

GRTensor is a very handy Maple package for doing calculations in General Relativity. Given a specific metric, it’s great at calculating the components of tensors. You can define your own tensors or use the predefined ones. You can even define your own metrics.

Unfortunately, getting it working on Mac OS X is a bit of a pain. This is due to a bug in GRTensor that has gone unfixed for quite a while. Fortunately, there is a straightforwarde solution.

Continue reading GRTensor: Metrics and Mac OS X

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