We present the results of the first search for gravitational wave bursts associated with high energy neutrinos. Together, these messengers could reveal new, hidden sources that are not observed by conventional photon astronomy, particularly at high energy. Our search uses neutrinos detected by the underwater neutrino telescope ANTARES in its 5 line configuration during the period January - September 2007, which coincided with the fifth and first science runs of LIGO and Virgo, respectively. The LIGO-Virgo data were analysed for candidate gravitational-wave signals coincident in time and direction with the neutrino events. No significant coincident events were observed. We place limits on the density of joint high energy neutrino - gravitational wave emission events in the local universe, and compare them with densities of merger and core-collapse events.

The linearized partial differential equation from the nonlinear partial differential equation which was proposed by Rudin, Osher and Fatemi [L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms] for solving image decomposition was introduced by Chambolle [A. Chambolle, An algorithm for total variation minimization and applications] and R. Acar and C.R. Vogel [R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems]. In this paper, we propose a method for solving the linearized partial differential equation and we show numerical results for denoising which demonstrate a significant improvement over other previous works.

The total variation is a useful method for solving noise problems (denoising) because the total variation is very effective for recovering blocky, possibly discontinuous, images from noise data. However, it is not a easy problem to find the true image without noise from the total variation. In this paper a new functional is introduced to find the true image without noise by using the minimizer of the total variation. We prove the convergence of the sequence induced from the modified functional in the iterative scheme, and show that our numerical denoising gives significant improvement over other previous works.

We study thermodynamic quantities and phase transitions of a spherically symmetric Schwarzschild black hole by taking into account the back reaction through the conformal anomaly of matter fields, and show that there exists an additional phase transition to the conventional Hawking-Page phase transition. The small black hole is more probable than the hot flat space above a second critical temperature, while it is less probable than the hot flat space in the classical Schwarzschild black hole. However, the unstable small black hole eventually should decay into the stable large black hole because the conformal anomaly does not change its thermodynamic stability.

In black hole thermodynamics of certain models, the thermodynamic first law may contain the pressure term. The corresponding entropy follows the area law whereas the thermodynamic energy is not the same with the black hole mass. If the pressure can be decomposed into two parts and recombined with the original thermodynamic quantities, then the thermodynamic energy becomes the black hole mass and the entropy satisfying the area law turns out to be the corrected entropy called the Wald entropy, respectively.

It is well known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths. One can then pose an interesting question: What is the Einstein equation from the gauge theory point of view? Or equivalently, what is the gauge theory object corresponding to Einstein manifolds? We show that the Einstein equations in four dimensions are precisely self-duality equations in Yang–Mills gauge theory and so Einstein manifolds correspond to Yang–Mills instantons in SO(4) = SU(2)_L × SU(2)_R gauge theory. Specifically, we prove that any Einstein manifold with or without a cosmological constant always arises as the sum of SU(2)_L instantons and SU(2)_R anti-instantons. This result explains why an Einstein manifold must be stable because two kinds of instantons belong to different gauge groups, instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay into a vacuum. We further illuminate the stability of Einstein manifolds by showing that they carry nontrivial topological invariants.

We report a search for gravitational waves from the inspiral, merger and ringdown of binary black holes (BBH) with total mass between 25 and 100 solar masses, in data taken at the LIGO and Virgo observatories between July 7, 2009 and October 20, 2010. The maximum sensitive distance of the detectors over this period for a $(20,20)M_{\odot }$ coalescence was 300 Mpc. No gravitational wave signals were found. We thus report upper limits on the astrophysical coalescence rates of BBH as a function of the component masses for nonspinning components, and also evaluate the dependence of the search sensitivity on component spins aligned with the orbital angular momentum. We find an upper limit at 90% confidence on the coalescence rate of BBH with nonspinning components of mass between 19 and $28M_{\odot }$ of $3.3\times {10}^{-7}$ mergers ${\mathrm{Mpc}}^{-3}{\mathrm{yr}}^{-1}$ .

The sensitivity of searches for astrophysical transients in data from the Laser Interferometer Gravitational-wave Observatory (LIGO) is generally limited by the presence of transient, non-Gaussian noise artifacts, which occur at a high enough rate such that accidental coincidence across multiple detectors is non-negligible. These “glitches” can easily be mistaken for transient gravitational-wave signals, and their robust identification and removal will help any search for astrophysical gravitational waves. We apply machine-learning algorithms (MLAs) to the problem, using data from auxiliary channels within the LIGO detectors that monitor degrees of freedom unaffected by astrophysical signals. Noise sources may produce artifacts in these auxiliary channels as well as the gravitational-wave channel. The number of auxiliary-channel parameters describing these disturbances may also be extremely large; high dimensionality is an area where MLAs are particularly well suited. We demonstrate the feasibility and applicability of three different MLAs: artificial neural networks, support vector machines, and random forests. These classifiers identify and re a substantial fraction of the glitches present in two different data sets: four weeks of LIGO’s fourth science run and one week of LIGO’s sixth science run. We observe that all three algorithms agree on which events are glitches to within 10% for the sixth-science-run data, and support this by showing that the different optimization criteria used by each classifier generate the same decision surface, based on a likelihood-ratio statistic. Furthermore, we find that all classifiers obtain similar performance to the benchmark algorithm, the ordered veto list, which is optimized to detect pairwise correlations between transients in LIGO auxiliary channels and glitches in the gravitational-wave data. This suggests that most of the useful information currently extracted from the auxiliary channels is already described by this model. Future performance gains are thus likely to involve additional sources of information, rather than improvements in the classification algorithms themselves. We discuss several plausible sources of such new information as well as the ways of propagating it through the classifiers into gravitational-wave searches.

Compact binary systems with neutron stars or black holes are one of the most promising sources for ground-based gravitational-wave detectors. Gravitational radiation encodes rich information about source physics; thus parameter estimation and model selection are crucial analysis steps for any detection candidate events. Detailed models of the anticipated waveforms enable inference on several parameters, such as component masses, spins, sky location and distance, that are essential for new astrophysical studies of these sources. However, accurate measurements of these parameters and discrimination of models describing the underlying physics are complicated by artifacts in the data, uncertainties in the waveform models and in the calibration of the detectors. Here we report such measurements on a selection of simulated signals added either in hardware or software to the data collected by the two LIGO instruments and the Virgo detector during their most recent joint science run, including a “blind injection” where the signal was not initially revealed to the collaboration. We exemplify the ability to extract information about the source physics on signals that cover the neutron-star and black-hole binary parameter space over the component mass range $1M_{\odot }–25M_{\odot }$ and the full range of spin parameters. The cases reported in this study provide a snapshot of the status of parameter estimation in preparation for the operation of advanced detectors.

We present the results of a directed search for continuous gravitational waves from unknown, isolated neutron stars in the Galactic center region, performed on two years of data from LIGO’s fifth science run from two LIGO detectors. The search uses a semicoherent approach, analyzing coherently 630 segments, each spanning 11.5 hours, and then incoherently combining the results of the single segments. It covers gravitational wave frequencies in a range from 78 to 496 Hz and a frequency-dependent range of first-order spindown values down to $-7.86\times {10}^{-8}\mathrm{Hz}/s$ at the highest frequency. No gravitational waves were detected. The 90% confidence upper limits on the gravitational wave amplitude of sources at the Galactic center are $\sim 3.35\times {10}^{-25}$ for frequencies near 150 Hz. These upper limits are the most constraining to date for a large-parameter-space search for continuous gravitational wave signals.