A note on gravitational wave extraction from binary simulations

In previous works, we developed a perturbative extrapolation formula to obtain gravitational waves at infinity from binary black hole simulations, based on the Regge-Wheeler-Zerilli formalism. In practice, this formula was basically derived in a background flat spacetime. We derive here an estimation of errors and an improved extrapolation formula by using the Teukolsky perturbative equation for a background Kerr spacetime. The improved formula requires knowledge about a mass and spin of the background spacetime.