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 different
ial 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.
We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of optical len
sing, can lead to the geometrical optics approximation being invalid, in which case a wave optical solution is necessary. In general, wave optical solutions can only be obtained numerically. We describe a computational method that is particularly well suited to numerical wave optics. This method enables us to compare the properties of several lens models for globular clusters without ever calling upon the geometrical optics approximation, though that approximation would sometimes have been valid. Finally, we estimate the probability that lensing by a globular cluster will significantly affect the detection, by ground-based laser interferometer detectors such as LIGO, of gravitational waves from an asymmetric neutron star in our galaxy, finding that the probability is insignificantly small.
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional programming te
chniques. By allowing functions to be directly represented as program variables in C++ code, the functional framework enables the mathematical formalism of Differential Geometry to be more closely reflected in GRworkbench . The powerful technique of `automatic differentiation has replaced numerical differentiation of the metric components, resulting in more accurate derivatives and an order-of-magnitude performance increase for operations relying on differentiation.
