With the recent break through in gravitational wave detections by LIGO/VIRGO, we are now witnessing the birth of gravitational wave astronomy. This coupled with the success of ESA's LISA pathfinder mission, has solidified the launch of ESA's future space based detector, LISA. One of the key sources for LISA are Extreme Massive Ratio Inspirals (EMRIs), however, as yet, there are no precise EMRI waveforms available. An avenue of great potential for their development lies in the self-force approximation scheme.
The self-force tackles Einstein's field equations with a perturbative expansion in the mass ratio; at zero order, the smaller mass follows the geodesic of the background or accompanying black hole, while at first order, it deviates from this geodesic, following an "effective" geodesic arising from interaction with its own field. As the particle's self-field "pushes" it off its geodesic, this is seen as a force acting on the particle - the so-called self-force. One of the key problems that immediately arise within the self-force model is the divergence of the field at the particle. To resolve this, a specific model of the singular field is employed - the Detweiler-Whiting singular field; this can then be subtracted from the retarded field, leaving a smooth regular field, which (by construction) is wholly responsible for the self-force.
In this talk, we give an overview of the current status of the self-force and how it interplays with other schemes in the goal of black hole binary modelling. We show the construction of the Detweiler-Whiting singular field and how it is employed in all current self-force calculations. We outline the future goals and research directions being pursued by the self-force community and their application to gravitational wave detection.