There are many on-going projects of gravitational wave detection in the world; LIGO, GEO600, VIRGO, KAGRA, which are ground-based laser interferometers, and there are some future space interferometer projects such as eLISA, DECIGO.

Detection of gravitational waves provides us with not only a direct experimental test of general relativity but also a new window to observe our universe. However, because the signals are expected to be very weak, so to use them as a new tool of observation, it is necessary to know theoretical waveforms. Once we know them, we may appeal to the matched filtering technique to extract source's information from gravitational wave signals.

For the ground-based and future space-based interferometer, the coalescences of compact object binaries are the most important sources of gravitational waves. The process of coalescence can be divided into three distinct phases; inspiral, merger and ringdown. We focus on gravitational waves during the inspiral phase.

Black hole perturbation is a powerful tool for the evalution of gravitational waves from a particle of small mass μ orbiting a black hole of mass M, assuming μ << M in this phase. Gravitationl perturbations of a black hole were first studied by Regge-Wheeler about 40 year ago. Later a master equation for perturbations of a Kerr BH was derived by Teukolsky and its equivalence to the Regge-Wheeler equation was shown by Chandrasekhar in the case of a Schwarzschild BH.

In the case the mass ratio of the objects composing a binary is extremely large, self-force correction is very important. Self-force correction is the correction to the force acting on the small mass body (which is treated as point-particle) that are induced by the field generated by the particle itself. However the self-force diverges at location of the particle, and hence should be regularized.

The purpose of this web is to show our calculation and summarize the results. One of the main advantages of the black hole perturbation approach is the successful implementation of a systematic post-Newtonian expansion technique. The method can be easily extended to any desired PN order, so we show the higher post-Newtonian calculations in this Web.