An efficient numerical calculation of gravitational waves from extreme mass ratio inspirals

Gravitational waves from extreme mass ratio inspirals are one of the important sources of LISA. We should calculate these waves so accurately that we can extract physical information of source by data analysis. Recently, we developed an efficient numerical method to compute gravitational waves from binary systems in which a point particle moves in circular orbits on the equatorial plane of the black hole. In this paper, we apply this method to compute gravitational waves from binary systems in which a point particle moves in general bound geodesic orbits of the black hole. We check the accuracy of our code using spherical symmetry of Schwarzschild black hole such that energy flux radiated by a point particle is independent of the inclination angle from the equatorial plane of black hole. We find that the accuracy of our code may be limited only by truncation of l, k and n -modes, where l is the degree of the spin-weighted spheroidal harmonics, and k and n are harmonics of the polar and radial motion, respectively. Then we evaluate the rate of change of three constants of motion, energy, angular momentum and the Carter constant, due to the emission of gravitational waves from a particle around Kerr black hole. This is the first time to compute the rate of change of the Carter constant using the adiabatic approximation. We also show that we can calculate gravitational waves accurately even in the case of high eccentric orbits. In this work, we truncate l mode up to 20 and estimated that relative accuracy of our numerical results are better than 10-5 even in the high eccentric case, e = 0.9. Our numerical code may be useful to make templates of extreme mass ratio inspirals.