Nonlinear r-modes in rapidly rotating relativistic stars

The r-mode instability in rotating relativistic stars has been shown recent ly to have important astrophysical implications, provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mech anisms. Here, we present the first study of nonlinear r-modes in isentropic , rapidly rotating relativistic stars, via 3D general-relativistic hydrodyn amical evolutions. We find that (1) on dynamical time scales, there is no s trong nonlinear coupling of r-modes to other modes at amplitudes of order o ne-the maximum r-mode amplitude is of order unity. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes. (3) The kinema tical drift associated with r-modes appears to be present in our simulation s, but confirmation requires more precise initial data.