Recovering the stationary phase condition for accurately obtaining scattering and tunneling times

The stationary phase method is often employed for computing tunneling {\em phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of this method without considering the barrier boundary effects leads to some misconceptions in the interpretation of the phase times. After reexamining the above barrier diffusion problem where we notice the wave packet collision necessarily leads to the possibility of multiple reflected and transmitted wave packets, we study the phase times for tunneling/reflecting particles in a framework where an idea of multiple wave packet decomposition is recovered. To partially overcome the analytical incongruities which rise up when tunneling phase time expressions are obtained, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a one dimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted waves.Comment: 32 pages, 5 figures, 1 tabl

Uric acid enhances longevity and endurance and protects the brain against ischemia

Among mammals, there is a positive correlation between serum uric acid (UA) levels and life span. Humans have high levels of UA because they lack a functional urate oxidase (UOX) enzyme that is present in shorter lived mammals. Here, we show that male and female mice with UOX haploinsufficiency exhibit an age-related elevation of UA levels, and that the life span of female but not male UOX+/− mice is significantly increased compared to wild-type mice. Serum UA levels are elevated in response to treadmill exercise in UOX+/− mice, but not wild-type mice, and the endurance of the UOX+/− mice is significantly greater than wild-type mice. UOX+/− mice exhibit elevated levels of brain-derived neurotrophic factor, reduced brain damage and improved functional outcome in a model of focal ischemic stroke. Levels of oxidative protein nitration and lipid peroxidation are reduced in muscle and brain tissues of UOX+/− mice under conditions of metabolic and oxidative stress (running in the case of muscle and ischemia in the case of the brain), consistent with prior evidence that UA can scavenge peroxynitrite and hydroxyl radical. Our findings reveal roles for UA in life span determination, endurance and adaptive responses to brain injury, and suggest novel approaches for protecting cells against injury and for optimizing physical performance.España, Ministerio de Educación, Cultura y Deporte EX2009–091

Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order

We derive the gravitational field and equations of motion of compact binary systems up to the 5/2 post-Newtonian approximation of general relativity (where radiation-reaction effects first appear). The approximate post-Newtonian gravitational field might be used in the problem of initial conditions for the numerical evolution of binary black-hole space-times. On the other hand we recover the Damour-Deruelle 2.5PN equations of motion of compact binary systems. Our method is based on an expression of the post-Newtonian metric valid for general (continuous) fluids. We substitute into the fluid metric the standard stress-energy tensor appropriate for a system of two point-like particles. We remove systematically the infinite self-field of each particle by means of the Hadamard partie finie regularization.Comment: 41 pages to appear in Physical Review

Detection of high energy X-rays from the galactic center region

Observations of the galactic center region made with the high energy X-ray detector on OSO-8 are discussed. A strong hard X-ray which was detected during these observations from the vicinity of the galactic center are examined. The counting rate spectrum and the photon number spectrum of the flux are determined. Comparisons with the high energy X-ray fluxes observed from sources in the region by others are discussed

Prospects for gravitational-wave observations of neutron-star tidal disruption in neutron-star/black-hole binaries

For an inspiraling neutron-star/black-hole binary (NS/BH), we estimate the gravity-wave frequency f_td at the onset of NS tidal disruption. We model the NS as a tidally distorted, homogeneous, Newtonian ellipsoid on a circular, equatorial geodesic around a Kerr BH. We find that f_td depends strongly on the NS radius R, and estimate that LIGO-II (ca. 2006-2008) might measure R to 15% precision at 140 Mpc (about 1 event/yr under current estimates). This suggests that LIGO-II might extract valuable information about the NS equation of state from tidal-disruption waves.Comment: RevTeX, 4 pages, 2 EPS figures. Revised slightly, corrected typo

Physical instrumental vetoes for gravitational-wave burst triggers

We present a robust strategy to \emph{veto} certain classes of instrumental glitches that appear at the output of interferometric gravitational-wave (GW) detectors.This veto method is `physical' in the sense that, in order to veto a burst trigger, we make use of our knowledge of the coupling of different detector subsystems to the main detector output. The main idea behind this method is that the noise in an instrumental channel X can be \emph{transferred} to the detector output (channel H) using the \emph{transfer function} from X to H, provided the noise coupling is \emph{linear} and the transfer function is \emph{unique}. If a non-stationarity in channel H is causally related to one in channel X, the two have to be consistent with the transfer function. We formulate two methods for testing the consistency between the burst triggers in channel X and channel H. One method makes use of the \emph{null-stream} constructed from channel H and the \emph{transferred} channel X, and the second involves cross-correlating the two. We demonstrate the efficiency of the veto by `injecting' instrumental glitches in the hardware of the GEO 600 detector. The \emph{veto safety} is demonstrated by performing GW-like hardware injections. We also show an example application of this method using 5 days of data from the fifth science run of GEO 600. The method is found to have very high veto efficiency with a very low accidental veto rate.Comment: Minor changes, To appear in Phys. Rev.

Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order

Gravitational waves generated by inspiralling compact binaries are investigated to the second--post-Newtonian (2PN) approximation of general relativity. Using a recently developed 2PN-accurate wave generation formalism, we compute the gravitational waveform and associated energy loss rate from a binary system of point-masses moving on a quasi-circular orbit. The crucial new input is our computation of the 2PN-accurate ``source'' quadrupole moment of the binary. Tails in both the waveform and energy loss rate at infinity are explicitly computed. Gravitational radiation reaction effects on the orbital frequency and phase of the binary are deduced from the energy loss. In the limiting case of a very small mass ratio between the two bodies we recover the results obtained by black hole perturbation methods. We find that finite mass ratio effects are very significant as they increase the 2PN contribution to the phase by up to 52\%. The results of this paper should be of use when deciphering the signals observed by the future LIGO/VIRGO network of gravitational-wave detectors.Comment: 43 pages, LaTeX-ReVTeX, no figures

Gravitational radiation from a particle in circular orbit around a black hole. V. Black-hole absorption and tail corrections

A particle of mass $\mu$ moves on a circular orbit of a nonrotating black hole of mass $M$. Under the restrictions $\mu/M \ll 1$ and $v \ll 1$, where $v$ is the orbital velocity, we consider the gravitational waves emitted by such a binary system. We calculate $\dot{E}$, the rate at which the gravitational waves remove energy from the system. The total energy loss is given by $\dot{E} = \dot{E}^\infty + \dot{E}^H$, where $\dot{E}^\infty$ denotes that part of the gravitational-wave energy which is carried off to infinity, while $\dot{E}^H$ denotes the part which is absorbed by the black hole. We show that the black-hole absorption is a small effect: $\dot{E}^H/\dot{E} \simeq v^8$. We also compare the wave generation formalism which derives from perturbation theory to the post-Newtonian formalism of Blanchet and Damour. Among other things we consider the corrections to the asymptotic gravitational-wave field which are due to wave-propagation (tail) effects.Comment: ReVTeX, 17 page

General relativistic dynamics of compact binaries at the third post-Newtonian order

The general relativistic corrections in the equations of motion and associated energy of a binary system of point-like masses are derived at the third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian expansion of the metric in harmonic coordinates at the 3PN approximation. The metric is parametrized by appropriate non-linear potentials, which are evaluated in the case of two point-particles using a Lorentzian version of an Hadamard regularization which has been defined in previous works. Distributional forms and distributional derivatives constructed from this regularization are employed systematically. The equations of motion of the particles are geodesic-like with respect to the regularized metric. Crucial contributions to the acceleration are associated with the non-distributivity of the Hadamard regularization and the violation of the Leibniz rule by the distributional derivative. The final equations of motion at the 3PN order are invariant under global Lorentz transformations, and admit a conserved energy (neglecting the radiation reaction force at the 2.5PN order). However, they are not fully determined, as they depend on one arbitrary constant, which reflects probably a physical incompleteness of the point-mass regularization. The results of this paper should be useful when comparing theory to the observations of gravitational waves from binary systems in future detectors VIRGO and LIGO.Comment: 78 pages, submitted to Phys. Rev. D, with minor modification

Time-frequency detection of Gravitational Waves

We present a time-frequency method to detect gravitational wave signals in interferometric data. This robust method can detect signals from poorly modeled and unmodeled sources. We evaluate the method on simulated data containing noise and signal components. The noise component approximates initial LIGO interferometer noise. The signal components have the time and frequency characteristics postulated by Flanagan and Hughes for binary black hole coalescence. The signals correspond to binaries with total masses between $45 M_\odot$ to $70 M_\odot$ and with (optimal filter) signal-to-noise ratios of 7 to 12. The method is implementable in real time, and achieves a coincident false alarm rate for two detectors $\approx$ 1 per 475 years. At this false alarm rate, the single detector false dismissal rate for our signal model is as low as 5.3% at an SNR of 10. We expect to obtain similar or better detection rates with this method for any signal of similar power that satisfies certain adiabaticity criteria. Because optimal filtering requires knowledge of the signal waveform to high precision, we argue that this method is likely to detect signals that are undetectable by optimal filtering, which is at present the best developed detection method for transient sources of gravitational waves.Comment: 24 pages, 5 figures, uses REVTE