We study oscillations of slowly rotating relativistic barotropic as well as non‐barotropic polytropic stars in the Cowling approximation, including first‐order rotational corrections. By taking into account the coupling between the polar and axial equations, we find that, in contrast with previous results, the m= 2r modes are essentially unaffected by the continuous spectrum and exist even for very relativistic stellar models. In order to solve the infinite system of coupled equations numerically we have to truncate it at some value lmax. Although the time‐dependent equations are regular and can be evolved numerically without any problems, the eigenvalue equations possess a singular structure, which is related to the existence of a continuous spectrum. This prevents the numerical computation of an eigenmode if its eigenfrequency falls inside the continuous spectrum. The properties of the latter depend strongly on the cut‐off value lmax and it can consist of several either disconnected or overlapping patches, which are broader the more relativistic the stellar model is. By discussing the dependence of the continuous spectrum as a function of both the cut‐off value lmax and the compactness M/R, we demonstrate how it affects the inertial modes. By evolving the time‐dependent equations we are able to show that some of the inertial modes can actually exist inside the continuous spectrum, while some cannot. For more compact and therefore more relativistic stellar models the width of the continuous spectrum increases strongly and consequently some of the inertial modes, which exist in less relativistic stars, disappear.

Spin induced precessional modulations of gravitational wave signals from supermassive black hole binaries can improve the estimation of luminosity distance to the source by space based gravitational wave missions like the Laser Interferometer Space Antenna (LISA). We study how this impacts the ablity of LISA to do cosmology, specifically, to measure the dark energy equation of state (EOS) parameter w. Using the ΛCDM model of cosmology, we show that observations of precessing binaries with mass ratio 10:1 by LISA, combined with a redshift measurement, can improve the determination of w up to an order of magnitude with respect to the non precessing case depending on the total mass and the redshift.

Observations of gravitational waves from massive binary black hole systems at cosmological distances can be used to search for a dependence of the speed of propagation of the waves on wavelength, and thereby to bound the mass of a hypothetical graviton. We study the effects of precessions of the spins of the black holes and of the orbital angular momentum on the process of parameter estimation based on the method of matched filtering of gravitational-wave signals vs. theoretical template waveforms. For the proposed space interferometer LISA, we show that precessions, and the accompanying modulations of the gravitational waveforms, are effective in breaking degeneracies among the parameters being estimated, and effectively restore the achievable graviton-mass bounds to levels obtainable from binary inspirals without spin. For spinning, precessing binary black hole systems of equal masses 10 6 M⊙ at 3 Gpc, the lower bounds on the graviton Compton wavelength achievable are of the order of 5 × 10 16 km.

Non-axisymmetric oscillations of differentially rotating stars are studied using both slow rotation and Cowling approximation. The equilibrium stellar models are relativistic polytropes where differential rotation is described by the relativistic j-constant rotation law. The oscillation spectrum is studied versus three main parameters: the stellar compactness M/R, the degree of differential rotation A and the number of maximun couplings ℓmax. It is shown that the rotational splitting of the non-axisymmetric modes is strongly enhached by increasing the compactness of the star and the degree of differential rotation. Finally, we investigate the relation between the fundamental quadrupole mode and the corotation band of differentially rotating stars.

The equations describing nonradial adiabatic oscillations of differentially rotating relativistic stars are derived in relativistic slow rotation approximation. The differentially rotating configuration is described by a perturbative version of the relativistic j-constant rotation law. Focusing on the oscillation properties of the stellar fluid, the adiabatic nonradial perturbations are studied in the Cowling approximation with a system of five partial differential equations. In these equations, differential rotation introduces new coupling terms between the perturbative quantites with respect to the uniformly rotating stars. In particular, we investigate the axisymmetric and barotropic oscillations and compare their spectral properties with those obtained in nonlinear hydrodynamical studies. The perturbative description of the differentially rotating background and the oscillation spectrum agree within a few percent with those of the nonlinear studies.PACS numbers: 04.40. Dg, 95.30.Sf, 97.10.Sj