Quasi-periodic oscillations of high density thick accretion disks orbiting a
Schwarzschild black hole have been recently addressed as interesting sources of
gravitational waves. The aim of this paper is to compare the gravitational
waveforms emitted from these sources when computed using (variations of) the
standard quadrupole formula and gauge-invariant metric perturbation theory. To
this goal we evolve representative disk models using an existing general
relativistic hydrodynamics code which has been previously employed in
investigations of such astrophysical systems. Two are the main results of this
work: First, for stable and marginally stable disks, no excitation of the black
hole quasi-normal modes is found. Secondly, we provide a simple, relativistic
modification of the Newtonian quadrupole formula which, in certain regimes,
yields excellent agreement with the perturbative approach. This holds true as
long as back-scattering of GWs is negligible. Otherwise, any functional form of
the quadrupole formula yields systematic errors of the order of 10%.Comment: 6 pages and 3 figures, RevTex, accepted for publication in Phys. Rev.
