Gravitational wave fluxes on generic orbits in near-extreme Kerr spacetime:Higher spin and large eccentricity

To accurately obtain the waveform template of gravitational waves, substantial computational resources and extremely high precision are often required. In a previous study, we employed the confluent Heun function to obtain an exact solution to the Teukolsky equation. This approach allowed us to efficiently and accurately calculate the gravitational wave flux for a particle in circular orbits around a Schwarzschild black hole. Building on this method, we now extend its application to calculate the asymptotic gravitational wave fluxes from a particle in generic orbits around a near-extreme Kerr black hole. Our extended method proves particularly effective in handling computational challenges associated with large eccentricities(e = 0.9), higher spins(a = 0.999), higher harmonic modes, and strong-field regions. The results we obtained significantly outperform those derived from the numerical integration method based on the Mano-Suzuki-Takasugi method.