Gravitational waves by a particle in circular orbits around a Schwarzschild black hole - 5.5 post-newtonian formula

Using the post-Newtonian (PN) expansion technique of the gravitational wave perturbation around a Schwarzschild black hole, Ne calculate analytically the energy flux of gravitational waves induced by a particle in circular orbits up to the 5.5PN order, i.e., O(upsilon(11)) beyond Newtonian. By comparing the formula with numerical data, we find that the error of the 5.5PN formula is about 4% when the particle is on the last stable circular orbit. We also estimate the error Delta N in the total cycle of gravitational waves from coalescing compact binaries in a laser interferometer's band produced by using the post-Newtonian approximations. We find that, as for the neutron star-black hole binaries, the 4.5PN approximation gives Delta N less than or similar to 1 for a black hole of mass M < 40M., while it gives Delta N greater than or similar to 1 for a black hole of mass M > 40M..