Hybrid approach to black hole perturbations from extended matter sources

Abstract

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.

Dynamics of magnetized relativistic tori oscillating around black holes

“…Although more sophisticated approaches involving perturbative techniques around black holes can be employed to study the gravitational‐wave emission from these tori (Nagar et al 2005; Ferrari, Gualtieri & Rezzolla 2006; Nagar et al 2007), we here resort to the simpler and less expensive use of the Newtonian quadrupole approximation (Zanotti et al 2003), which has been suitably modified to account for the presence of a magnetic field, as done by Kotake et al (2004). In particular, the quadrupole wave amplitude A E2 20 , which is the second time derivative of the mass‐quadrupole moment, is computed through the ‘stress formula’ (Obergaulinger et al 2006) …”

Quasi-normal modes and gravitational wave astronomy

“…QNMs excitation has also been shown to give a strong contribution to the signal emitted after the core collapse of a rotating NS to a Kerr black hole [58]. Moreover, in [59,60] the gravitational emission of a black hole perturbed by a thick, oscillating accretion disk has been studied; in a subsequent paper [61] it has been shown that if the disk is extremely dense, black hole oscillations can be excited, even though, due to the symmetry of the source, only by a small amount. All numerical simulations of astrophysical processes in which QNMs are excited show that the leading contribution belong to the lowest frequency, = 2 mode.…”

Quasi-Normal Modes and Gravitational Wave Astronomy

“…Quasi-normal modes excitation has also been shown to give a strong contribution to the signal emitted after the core collapse of a rotating neutron star to a Kerr black hole [38]. Moreover, in [39] the gravitational emission of a black hole perturbed by a thick, oscillating accretion disk has been studied; in a subsequent paper [40] it has been shown that if the disk is extremely dense, black hole oscillations can be excited, even though, due to the symmetry of the source, only by a small amount. All numerical simulations of astrophysical processes in which QNMs are excited show that the leading contribution belong to the lowest frequency, ℓ = 2 mode.…”