Scalar Fields in Numerical General Relativity

Abstract

This set of notes was designed to accompany two hours of lectures and practical exercises at the New Horizons for Psi workshop https://strong-gr.com/new-horizons-for-psi, entitled "Studying fundamental fields with numerical relativity".Numerical relativity (NR) is a tool used to help understand the behaviours of metric and matter fields in dynamical, strong gravity situations. It has been used to study a range of situations involving fundamental fields, including superradiance, modified gravity, dynamical friction, dark matter accretion and early universe cosmology. We will hear more about these in the workshop. The purpose of this course is to provide you with some background and hands on experience in numerical relativity that will help you to better understand the possibilities and limitations provided by this tool.We will use the code engrenage. This is a spherically symmetric code designed for teaching NR that uses the reference metric framework and a dynamical gauge. The code includes a scalar field obeying the Klein Gordon (KG) equation for a minimally coupled spin 0 field as the matter source of the metric curvature. The version of the code we will use in the course can be found here: https://github.com/GRTLCollaboration/engrenage/tree/NewHorizonsForPsi. The code is based on the formalism in the papers [1, 2, 3] and many people have contributed to its development -please see the acknowledgements for more details.My assumption for these notes is that people know GR and may have come across the ADM decomposition, but don't know numerical methods or numerical relativity itself. For those who are already familiar with numerical methods and the ADM decomposition you can skip directly to the exercises and try to go as far as you can with them. There is more there than you can do in 2 hours, so feel free to pick and choose exercises you feel most motivated to try, they can all be completed independently of each other. For more details see the papers above or the key NR texts [4,5,6,7,8] ([5] is particularly good for beginners). The wiki for the course also provides relevant background material: https://github.com/GRTLCollaboration/engrenage/wiki/New-Horizons-for-Psi-workshop.Disclaimer: The engrenage code was not designed to be a good example of optimised python usage.The goal was to write a code where some non trivial physical examples could be studied and users could get an overview of the different parts of a numerical relativity code with a dynamical gauge, without the obfuscation that arises due to the optimisation and HPC requirements of a typical research code like its parent GRChombo [9]. However, thanks to input from others it now has quite good performance and I have used it successfully for several testing and research projects. Masters students in particular benefit from the simple python format, which means they can get started quickly with implementing actual physics. 1 .1 The original working name of the code was BabyGRChombo, engrenage (a system of gears) was chosen because it captures the idea o...

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