Nearly a century after Einstein first predicted the existence of gravitational waves, a global network of Earth-based gravitational wave observatories [1, 2, 3, 4] is seeking to directly detect this faint radiation using precision laser interferometry. Photon shot noise, due to the quantum nature of light, imposes a fundamental limit on the attometre-level sensitivity of the kilometre-scale Michelson interferometers deployed for this task. Here, we inject squeezed states to improve the performance of one of the detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) beyond the quantum noise limit, most notably in the frequency region down to 150 Hz, critically important for several astrophysical sources, with no deterioration of performance observed at any frequency. With the injection of squeezed states, this LIGO detector demonstrated the best broadband sensitivity to gravitational waves ever achieved, with important implications for observing the gravitational-wave Universe with unprecedented sensitivity

In many astrophysical problems, it is important to understand the behavior of functions that come from rotating (Kerr) black hole orbits. It can be particularly useful to work with the frequency domain representation of those functions, in order to bring out their harmonic dependence upon the fundamental orbital frequencies of Kerr black holes. Although, as has recently been shown by W. Schmidt, such a frequency domain representation must exist, the coupled nature of a black hole orbit's $r$ and $\theta$ motions makes it difficult to construct such a representation in practice. Combining Schmidt's description with a clever choice of timelike coordinate suggested by Y. Mino, we have developed a simple procedure that sidesteps this difficulty. One first Fourier expands all quantities using Mino's time coordinate $\lambda$. In particular, the observer's time $t$ is decomposed with $\lambda$. The frequency domain description is then built from the $\lambda$-Fourier expansion and the expansion of $t$. We have found this procedure to be quite simple to implement, and to be applicable to a wide class of functionals. We test the procedure using a simple test function, and then apply it in a particularly interesting case, the Weyl curvature scalar $\psi_4$ used in black hole perturbation theory.Comment: 16 pages, 2 figures. Submitted to Phys Rev D. New version gives a vastly improved algorithm due to Drasco for computing the Fourier transforms. Drasco has been added as an author. Also fixed some references and exterminated a small herd of typos; final published versio

We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M progenitor was studied in 2D by Müller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low--mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.

Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes. The orbits we consider are generic - simultaneously eccentric and inclined. The waves can be described as having radial, polar, and azimuthal "voices", each of which can be made to dominate by varying eccentricity and inclination. Although each voice is generally apparent in the waveform, the radial voice is prone to overpowering the others. We also compute the radiative fluxes of energy and axial angular momentum at infinity and through the event horizon. These fluxes, coupled to a prescription for the radiative evolution of the Carter constant, will be used in future work to adiabatically evolve through a sequence of generic orbits. This will enable the calculation of inspiral waveforms that, while lacking certain important features, will approximate those expected from astrophysical extreme mass ratio captures sufficiently well to aid development of measurement algorithms on a relatively short timescale.Comment: Minor changes in response to comments from readers, referees, and editors. Final version, as it will appear in Physical Review D. Raw data and a small program which will convert the data into waveforms lasting for arbitrary lengths of time can be found at http://gmunu.mit.edu/sdrasco/snapshot