However, since an EMRI will go through many cycles of gravitational waves (~105) before making the plunge into the central supermassive black hole, it should still be possible to extract the signal using matched filtering. In this process, the observed signal is compared with a template of the expected signal, amplifying components that are similar to the theoretical template. To be effective this requires accurate theoretical predictions for the wave forms of the gravitational waves produced by an extreme mass ratio inspiral. This, in turn, requires accurate modelling of the trajectory of the EMRI. The equations of motion in general relativity are notoriously hard to solve analytically. Consequently, one needs to use some sort of approximation scheme. Extreme mass ratio inspirals are well suited for this, as the mass of the compact object is much smaller than that of the central supermassive black hole. This allows it to be ignored or treated perturbatively. One common approach is to expand the equations of motion for an object in terms of its velocity divided by the speed of light, "v"/"c". This approximation is very effective if the velocity is very small, but becomes rather inaccurate if "v"/"c" becomes larger than about 0.3. For binary systems of comparable mass, this limit is not reached until the last few cycles of the orbit. EMRIs, however, spend their last thousand to a million cycles in this regime, making the post-Newtonian expansion an inappropriate tool. Another approach is to completely solve the equations of motion numerically. The non-linear nature of the theory makes this very challenging, but significant success has been achieved in numerically modelling the final phase of the inspiral of binaries of comparable mass. The large number of cycles of an EMRI make the purely numerical approach prohibitively expensive in terms of computing time. The large value of the mass ratio in an EMRI opens another avenue for approximation: expansion in one over the mass ratio. To zeroth order, the path of the lighter object will be a geodesic in the Kerr spacetime generated by the supermassive black hole. Corrections due to the finite mass of the lighter object can then be included, order-by-order in the mass ratio, as an effective force on the object. This effective force is known as the gravitational self force. In the last decade or so, a lot of progress has been made in calculating the gravitational self force for EMRIs. Numerical codes are available to calculate the gravitational self force on any bound orbit around a non-rotating (Schwarzschild) black hole.