Gravitational waves; ripples in spacetime as predicted by Einstein’s theory of relativity. Einstein saw masses as sources of energy that curved spacetime around them pulling everything inwards like the incline of a hill. When extremely compact objects like black holes or neutron stars get too close, a violent interaction occurs between their fields as they merge - this clash of curvature results in smaller waves rippling out across the universe. The first detection of gravitational waves occurred in September 2015 and marked the birth of gravitational wave astronomy - not only giving us a new window through which to look at the universe but it marks an united effort by researchers across the globe in accomplishing a common goal - insight into the world in which we all live.
To enable detection, one must calculating gravitational waveforms. The current Earth detectors, aLIGO and aVIRGO are sensitive to binaries (black holes and/or neutron stars) with similar masses. Waveforms in this regime are well known, however, a key aim of gravitational wave detectors is to test Einstein’s theory of general relativity. To do so conclusively, one needs waveforms for alternative theories; these currently exist only to first post-Newtonian accuracy (1PN), an approximations that assumes a slow-moving system. However, for gravitational wave detection, it is well established that one requires second order post-Newtonian (2PN) calculations – this carries over to waveforms for alternative theories of gravity. We are currently calculating the 2PN waveform for scalar-tensor gravity, a theory that differs from General Relativity by only a varying Gravitational `constant’. This, combined with the detection data of the binary neutron star can be used to test general relativity in the strong field regime.
All gravitational wave detectors are currently on Earth and hence limited to higher-frequency gravitational waves by the tectonic plate movements – for low frequency, one most have space-based detectors, like LISA, the future ESA detector. LISA will detect EMRI’s, Extreme Mass Ratio Inspirals - these are thought to form when a `small' stellar mass black hole (the same mass as our sun) is bumped into the grasp of a supermassive black hole (like that living at the centre of our galaxy). Unfortunately, we do not have EMRI waveforms. The self-force, which expands in the mass ratio, is perfect for tackling this problem. At zero order, the smaller body behaves massless and follows the curved spacetime of the larger black hole. At first order, it deviates due to interaction with its own field. This field has a singularity at the particle; however, one can model a singular field, that captures this singularity without affecting motion, and remove it. A more accurate singular field allows a more efficient (increased accuracy and speed) self-force calculation – in a field of producing banks of waveforms with costly computations, this is a necessity for self-force calculations.
To successfully produce waveforms, the self-force community requires highly accurate first order calculations (enhanced by accurate singular fields), second order calculations and a method to evolve the orbit. On calculating the self-force, one knows how much the body’s own field pushes it off its `natural’ path, depicted by the supermassive black hole. One then includes this force on the particle to calculate the self-force at the next step – hence evolving the orbit. This project deals with production of the singular field for first order self-force and orbit evolution codes - this allows more efficient calculations. This project is also involves the second order self-force - a calculation that has not yet been accomplished. In this manner, this project is assisting, on every front, the effort of self-force calculations towards EMRI waveforms.
