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Gravitational fields invariant for a 2-dimensional Lie algebra of Killing fields [ X,Y] =Y, with Y of light type, are analyzed. The conditions for them to represent gravitational waves are verified and the definition of energy and polarization is addressed; realistic generating sources are described.
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Non-vacuum exact gravitational waves invariant for a non Abelian two-dimensional Lie algebra generated by two Killing fields whose commutator is of light type, are described. The polarization of these waves, already known from previous works, is related to the sources. Non vacuum exact gravitational waves admitting only one Killing field of light type are also discussed.
Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.
We consider the cross-correlation search for periodic GWs and its potential application to the LMXB Sco X-1. This method coherently combines data from different detectors at the same time, as well as different times from the same or different detectors. By adjusting the maximum time offset between a pair of data segments to be coherently combined, one can tune the method to trade off sensitivity and computing costs. In particular, the detectable signal amplitude scales as the inverse fourth root of this coherence time. The improvement in amplitude sensitivity for a search with a coherence time of 1hr, compared with a directed stochastic background search with 0.25Hz wide bins is about a factor of 5.4. We show that a search of 1yr of data from Advanced LIGO and Advanced Virgo with a coherence time of 1hr would be able to detect GWs from Sco X-1 at the level predicted by torque balance over a range of signal frequencies from 30-300Hz; if the coherence time could be increased to 10hr, the range would be 20-500Hz. In addition, we consider several technical aspects of the cross-correlation method: We quantify the effects of spectral leakage and show that nearly rectangular windows still lead to the most sensitive search. We produce an explicit parameter-space metric for the cross-correlation search in general and as applied to a neutron star in a circular binary system. We consider the effects of using a signal template averaged over unknown amplitude parameters: the search is sensitive to a combination of the intrinsic signal amplitude and the inclination of the neutron star rotation axis, and the peak of the expected detection statistic is systematically offset from the true signal parameters. Finally, we describe the potential loss of SNR due to unmodelled effects such as signal phase acceleration within the Fourier transform timescale and gradual evolution of the spin frequency.
We present results of a search for continuously-emitted gravitational radiation, directed at the brightest low-mass X-ray binary, Scorpius X-1. Our semi-coherent analysis covers 10 days of LIGO S5 data ranging from 50-550 Hz, and performs an incoherent sum of coherent $mathcal{F}$-statistic power distributed amongst frequency-modulated orbital sidebands. All candidates not removed at the veto stage were found to be consistent with noise at a 1% false alarm rate. We present Bayesian 95% confidence upper limits on gravitational-wave strain amplitude using two different prior distributions: a standard one, with no a priori assumptions about the orientation of Scorpius X-1; and an angle-restricted one, using a prior derived from electromagnetic observations. Median strain upper limits of 1.3e-24 and 8e-25 are reported at 150 Hz for the standard and angle-restricted searches respectively. This proof of principle analysis was limited to a short observation time by unknown effects of accretion on the intrinsic spin frequency of the neutron star, but improves upon previous upper limits by factors of ~1.4 for the standard, and 2.3 for the angle-restricted search at the sensitive region of the detector.
Motivated by the next generation of gravitational wave (GW) detectors, we study the wave mechanics of a twisted light beam in the GW perturbed spacetime. We found a new gravitational dipole interaction of photons and gravitational waves. Physically, this interaction is due to coupling between the angular momentum of twisted light and the GW polarizations. We demonstrate that for the higher-order Laguerre-Gauss (LG) modes, this coupling effect makes photons undergoing dipole transitions between different orbital-angular-momentum(OAM) eigenstates, and leads to some measurable optical features in the 2-D intensity pattern. It offers an alternative way to realize precision measurements of the gravitational waves, and enables us to extract more information about the physical properties of gravitational waves than the current interferometry. With a well-designed optical setup, this dipole interaction is expected to be justified in laboratories.
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