The first numerical study of axial (toroidal) pulsation modes of a slowly rotating relativistic star is presented. The calculation includes terms of first order in $\epsilon \equiv \Omega \sqrt{R^3/M}<<1$ ($R$ is the radius, $M$ is the mass and $\Omega$ is the rotation frequency of the star), and accounts for effects due to the coriolis force. Effects due to the centrifugal flattening of the star enter at order $\epsilon^2$ and are not included in the analysis. It is shown that increased rotation tends to decrease the damping times for prograde modes, while retrograde become longer lived. Specifically, we show that rotation affects the axial gravitational-wave $w$-modes in this way. We also present the first relativistic calculation of the so-called $r$-modes (analogous to Rossby waves in the Earth's oceans). These have frequencies of the same order of magnitude as the rotation frequency of the star. The presented results indicate that the $r$-modes are unstable due to the emission of gravitational radiation for \underline{all} rotating perfect fluid stars. This is interesting since the previously considered gravitational-wave instability associated with (for example) the $f$-mode of the star sets in at a critical rotation rate. Because they are unstable also for the slowest rotating stars the $r$-modes may well be of considerable astrophysical importance.

We present new results for pulsating neutron stars. We have calculated the eigenfrequencies of the modes that one would expect to be the most importa

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.

The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics f