A hybrid approach to black hole perturbations from extended matter   sources
  We present a new method for the calculation of black hole perturbations induced by extended sources in which the solution of the nonlinear hydrodynamics equations is coupled to a perturbative method based on Regge-Wheeler/Zerilli and Bardeen-Press-Teukolsky equations when these are solved in the frequency domain. In contrast to alternative methods in the time domain which may be unstable for rotating black-hole spacetimes, this approach is expected to be stable as long as an accurate evolution of the matter sources is possible. Hence, it could be used under generic conditions and also with sources coming from three-dimensional numerical relativity codes. As an application of this method we compute the gravitational radiation from an oscillating high-density torus orbiting around a Schwarzschild black hole and show that our method is remarkably accurate, capturing both the basic quadrupolar emission of the torus and the excited emission of the black hole. 
Valeria Ferrari, Leonardo Gualtieri, Luciano Rezzolla