Abstract:
In the present paper we examine gravitational wave asteroseismology relations for f-modes of rapidly rotating neutron stars. An approach different to the previous studies is employed - first, the moment of inertia is used instead of the stellar radius, and second, the normalization of the oscillation frequencies and damping times is different. It was shown that in the non-rotating case this can lead to a much stronger equation of state independence and our goal is to generalize the static relations to the rapidly rotating case and values of the spherical mode number $l\ge2$. We employ realistic equations of state that cover a very large range of stiffness in order to check better the universality of the relations. At the end we explore the inverse problem, i.e. obtain the neutron star parameters from the observed gravitational frequencies and damping times. It turns out that with this new set of relations we can solve the inverse problem with a very good accuracy using three frequencies that was not possible in the previous studies where one needs also the damping times. The asteroseismology relations are also particularly good for the massive rapidly rotating models that are subject to secular instabilities.

Abstract:
Using the nuclear equation of states for a large variety of relativistic and non-relativistic force parameters, we calculate the static and rotating masses and radii of neutron stars. From these equation of states, we also evaluate the properties of rotating neutron stars, such as rotational and gravitational frequencies, moment of inertia, quadrupole deformation parameter, rotational ellipcity and gravitational wave strain amplitude. The estimated gravitational wave strain amplitude of the star is found to be $\sim 10^{-23}$.

Abstract:
Gravitational waves are tiny disturbances in space-time and are a fundamental, although not yet directly confirmed, prediction of General Relativity. Rapidly rotating neutron stars are one of the possible sources of gravitational radiation dependent upon pulsar's rotational frequency, details of the equation of state of stellar matter, and distance to detector. Applying an equation of state with symmetry energy constrained by recent nuclear laboratory data, we set an upper limit on the strain-amplitude of gravitational waves emitted by rapidly rotating neutron stars.

Abstract:
In this review we examine the dynamics and gravitational wave detectability of rotating strained neutron stars. The discussion is divided into two halves: triaxial stars, and precessing stars. We summarise recent work on how crustal strains and magnetic fields can sustain triaxiality, and suggest that Magnus forces connected with pinned superfluid vortices might contribute to deformation also. The conclusions that could be drawn following the successful gravitational wave detection of a triaxial star are discussed, and areas requiring further study identified. The latest ideas regarding free precession are then outlined, and the recent suggestion of Middleditch et al (2000a,b) that the remnant of SN1987A contains a freely precessing star, spinning-down by gravitational wave energy loss, is examined critically. We describe what we would learn about neutron stars should the gravitational wave detectors prove this hypothesis to be correct.

Abstract:
Remnants of neutron-star mergers are essentially massive, hot, differentially rotating neutron stars, which are initially strongly oscillating. They represent a unique probe for high-density matter because the oscillations are detectable via gravitational-wave measurements and are strongly dependent on the equation of state. The impact of the equation of state is apparent in the frequency of the dominant oscillation mode of the remnant. For a fixed total binary mass a tight relation between the dominant postmerger frequency and the radii of nonrotating neutron stars exists. Inferring observationally the dominant postmerger frequency thus determines neutron star radii with high accuracy of the order of a few hundred meters. By considering symmetric and asymmetric binaries of the same chirp mass, we show that the knowledge of the binary mass ratio is not critical for this kind of radius measurements. We summarize different possibilities to deduce the maximum mass of nonrotating neutron stars. We clarify the nature of the three most prominent features of the postmerger gravitational-wave spectrum and argue that the merger remnant can be considered to be a single, isolated, self-gravitating object that can be described by concepts of asteroseismology. The understanding of the different mechanisms shaping the gravitational-wave signal yields a physically motivated analytic model of the gravitational-wave emission, which may form the basis for template-based gravitational-wave data analysis. We explore the observational consequences of a scenario of two families of compact stars including hadronic and quark stars. We find that this scenario leaves a distinctive imprint on the postmerger gravitational-wave signal. In particular, a strong discontinuity in the dominant postmerger frequency as function of the total mass will be a strong indication for two families of compact stars. (abridged)

Abstract:
We present a self-consistent, relativistic model of rapidly rotating neutron stars describing their exterior gravitational field. This is achieved by matching the new solution of Einstein's field equations found by Manko et al. (2000) and the numerical results for the interior of neutron stars with different equations of state calculated by Cook et al. (1994). This matching process gives constraints for the choice of the five parameters of the vacuum solution. Then we investigate some properties of the gravitational field of rapidly rotating neutron stars with these fixed parameters.

Abstract:
The background of gravitational waves produced by the ensemble of rotating neutron stars (which includes pulsars, magnetars and gravitars) is investigated. A formula for \Omega(f) (commonly used to quantify the background) is derived, properly taking into account the time evolution of the systems since their formation until the present day. Moreover, the formula allows one to distinguish the different parts of the background: the unresolvable (which forms a stochastic background) and the resolvable. Several estimations of the background are obtained, for different assumptions on the parameters that characterize neutron stars and their population. In particular, different initial spin period distributions lead to very different results. For one of the models, with slow initial spins, the detection of the background can be rejected. However, other models do predict the detection of the background by the future ground-based gravitational wave detector ET. A robust upper limit for the background of rotating neutron stars is obtained; it does not exceed the detection threshold of two cross-correlated Advanced LIGO interferometers. If gravitars exist and constitute more than a few percent of the neutron star population, then they produce an unresolvable background that could be detected by ET. Under the most reasonable assumptions on the parameters characterizing a neutron star, the background is too faint. Previous papers have suggested neutron star models in which large magnetic fields (like the ones that characterize magnetars) induce big deformations in the star, which produce a stronger emission of gravitational radiation. Considering the most optimistic (in terms of the detection of gravitational waves) of these models, an upper limit for the background produced by magnetars is obtained; it could be detected by ET, but not by BBO or DECIGO.

Abstract:
Gravitational radiation drives an instability in the r-modes of young rapidly rotating neutron stars. This instability is expected to carry away most of the angular momentum of the star by gravitational radiation emission, leaving a star rotating at about 100 Hz. In this paper we model in a simple way the development of the instability and evolution of the neutron star during the year-long spindown phase. This allows us to predict the general features of the resulting gravitational waveform. We show that a neutron star formed in the Virgo cluster could be detected by the LIGO and VIRGO gravitational wave detectors when they reach their ``enhanced'' level of sensitivity, with an amplitude signal-to-noise ratio that could be as large as about 8 if near-optimal data analysis techniques are developed. We also analyze the stochastic background of gravitational waves produced by the r-mode radiation from neutron-star formation throughout the universe. Assuming a substantial fraction of neutron stars are born with spin frequencies near their maximum values, this stochastic background is shown to have an energy density of about 10^-9 of the cosmological closure density, in the range 20 Hz to 1 kHz. This radiation should be detectable by ``advanced'' LIGO as well.

Abstract:
Rapidly rotating neutron stars in Low Mass X-ray Binaries have been proposed as an interesting source of gravitational waves. In this chapter we present estimates of the gravitational wave emission for various scenarios, given the (electromagnetically) observed characteristics of these systems. First of all we focus on the r-mode instability and show that a 'minimal' neutron star model (which does not incorporate exotica in the core, dynamically important magnetic fields or superfluid degrees of freedom), is not consistent with observations. We then present estimates of both thermally induced and magnetically sustained mountains in the crust. In general magnetic mountains are likely to be detectable only if the buried magnetic field of the star is of the order of $B\approx 10^{12}$ G. In the thermal mountain case we find that gravitational wave emission from persistent systems may be detected by ground based interferometers. Finally we re-asses the idea that gravitational wave emission may be balancing the accretion torque in these systems, and show that in most cases the disc/magnetosphere interaction can account for the observed spin periods.

Abstract:
We provide details and present additional results on the numerical study of the gravitational-wave emission from the collapse of neutron stars to rotating black holes in three dimensions. More specifically, we concentrate on the advantages and disadvantages of the use of the excision technique and on how alternative approaches to that of excision can be successfully employed. Furthermore, as a first step towards source-characterization, we present a systematic discussion of the influence that rotation and different perturbations have on the waveforms and hence on the energy emitted in gravitational waves.