Numerical experimentation within GRworkbench

TL;DR

GRworkbench is a software tool for numerical experiments in General Relativity, now extended with advanced numerical methods and tools to simulate complex physical scenarios, addressing limitations of traditional analysis.

Contribution

The paper introduces significant extensions to GRworkbench, including a rewritten differential geometric engine and new numerical experimentation tools, enabling detailed simulations without simplifying assumptions.

Findings

The claim about measuring the Milky Way's mass was investigated and found to be an artifact of approximations.

Numerical modeling provided an accurate estimate of the physical effect without simplifying assumptions.

The limitations of traditional pen-and-paper analysis in General Relativity were demonstrated.

Abstract

The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. This year, GRworkbench has been significantly extended to facilitate numerical experimentation. The numerical differential geometric engine has been rewritten using functional programming techniques, enabling fundamental concepts to be directly represented as variables in the C++ code of GRworkbench. Sophisticated general numerical methods have replaced simpler specialised algorithms. Various tools for numerical experimentation have been implemented, allowing for the simulation of complex physical situations. A recent claim, that the mass of the Milky Way can be measured using a small interferometer located on the surface of the Earth, has been investigated, and found to be an artifact of the approximations employed in the analysis. This difficulty is symptomatic of the limitations of traditional pen-and-paper analysis in General Relativity, which was the motivation behind the original development of GRworkbench. The physical situation pertaining to the claim has been modelled in a numerical experiment in GRworkbench, without the necessity of making any simplifying assumptions, and an accurate estimate of the effect has been obtained.