Wall quenching of laminar flame propagation

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Components of the gravitational force in the field of a gravitational wave

Gravitational waves bring about the relative motion of free test masses. The detailed knowledge of this motion is important conceptually and practically, because the mirrors of laser interferometric detectors of gravitational waves are essentially free test masses. There exists an analogy between the motion of free masses in the field of a gravitational wave and the motion of free charges in the field of an electromagnetic wave. In particular, a gravitational wave drives the masses in the plane of the wave-front and also, to a smaller extent, back and forth in the direction of the wave's propagation. To describe this motion, we introduce the notion of `electric' and `magnetic' components of the gravitational force. This analogy is not perfect, but it reflects some important features of the phenomenon. Using different methods, we demonstrate the presence and importance of what we call the `magnetic' component of motion of free masses. It contributes to the variation of distance between a pair of particles. We explicitely derive the full response function of a 2-arm laser interferometer to a gravitational wave of arbitrary polarization. We give a convenient description of the response function in terms of the spin-weighted spherical harmonics. We show that the previously ignored `magnetic' component may provide a correction of up to 10 %, or so, to the usual `electric' component of the response function. The `magnetic' contribution must be taken into account in the data analysis, if the parameters of the radiating system are not to be mis-estimated.Comment: prints to 29 pages including 9 figures, new title, additional explanations and references in response to referee's comments, to be published in Class. Quant. Gra

Gravitational wave scintillation by a stellar cluster

The diffraction effects on gravitational waves propagating through a stellar cluster are analyzed in the relevant approximation of Fresnel diffraction limit. We find that a gravitational wave scintillation effect - similar to the radio source scintillation effect - comes out naturally, implying that the gravitational wave intensity changes in a characteristic way as the observer moves.Comment: 9 pages, in press in IJMP

Geometrical Expression for the Angular Resolution of a Network of Gravitational-Wave Detectors

We report for the first time general geometrical expressions for the angular resolution of an arbitrary network of interferometric gravitational-wave (GW) detectors when the arrival-time of a GW is unknown. We show explicitly elements that decide the angular resolution of a GW detector network. In particular, we show the dependence of the angular resolution on areas formed by projections of pairs of detectors and how they are weighted by sensitivities of individual detectors. Numerical simulations are used to demonstrate the capabilities of the current GW detector network. We confirm that the angular resolution is poor along the plane formed by current LIGO-Virgo detectors. A factor of a few to more than ten fold improvement of the angular resolution can be achieved if the proposed new GW detectors LCGT or AIGO are added to the network. We also discuss the implications of our results for the design of a GW detector network, optimal localization methods for a given network, and electromagnetic follow-up observations.Comment: 13 pages, for Phys. Rev.

Quantum variational measurement in the next generation gravitational-wave detectors

A relatively simple method of overcoming the Standard Quantum Limit in the next-generation Advanced LIGO gravitational wave detector is considered. It is based on the quantum variational measurement with a single short (a few tens of meters) filter cavity. Estimates show that this method allows to reduce the radiation pressure noise at low frequencies ($<100 \mathrm{Hz}$) to the level comparable with or smaller than the low-frequency noises of non-quantum origin (mirrors suspension noise, mirrors internal thermal noise, and gravity gradients fluctuations).Comment: 12 pages, 4 figures; NSNS SNR estimates added; misprints correcte

Gravitating Fluxbranes

We consider the effect that gravity has when one tries to set up a constant background form field. We find that in analogy with the Melvin solution, where magnetic field lines self-gravitate to form a flux-tube, the self-gravity of the form field creates fluxbranes. Several exact solutions are found corresponding to different transverse spaces and world-volumes, a dilaton coupling is also considered.Comment: 14 pages, 5 figure

Low-frequency gravitational radiation from coalescing massive black hole binaries in hierarchical cosmologies

We compute the expected gravitational wave signal from coalescing massive black hole (MBH) binaries at the center of galaxies in a hierarchical structure formation scenario in which seed holes of intermediate mass form far up in the dark halo merger tree. The merger history of DM halos and MBHs is followed from z=20 to the present in a LCDM cosmology. MBHs get incorporated through halo mergers into larger and larger structures, sink to the center owing to dynamical friction against the DM background, accrete cold material in the merger remnant, and form MBH binary systems. Stellar dynamical interactions cause the hardening of the binary at large separations, while gravitational wave emission takes over at small radii and leads to the final coalescence of the pair. The integrated emission from inspiraling MBH binaries results in a gravitational wave background (GWB). The characteristic strain spectrum has the standard h_c(f)\propto f^{-2/3} behavior only in the range 1E-9<f<1E-6 Hz. At lower frequencies the orbital decay of MBH binaries is driven by the ejection of background stars, and h_c(f) \propto f. At higher frequencies, f>1E-6 Hz, the strain amplitude is shaped by the convolution of last stable circular orbit emission. We discuss the observability of inspiraling MBH binaries by the planned LISA. Over a 3-year observing period LISA should resolve this GWB into discrete sources, detecting ~60 (~250) individual events above a S/N=5 (S/N=1) confidence level. (Abridged)Comment: 11 pages, 8 figues. Revised version accepted to be published in ApJ Discussion on number counts corrected and expande

Classical stability and quantum instability of black-hole Cauchy horizons

For a certain region of the parameter space $\{M,e,\Lambda\}$, the Cauchy horizon of a (charged) black hole residing in de Sitter space is classically stable to gravitational perturbations. This implies that, when left to its own devices, classical theory is unable to retain full predictive power: the evolution of physical fields beyond the Cauchy horizon is not uniquely determined by the initial conditions. In this paper we argue that the Cauchy horizon of a Reissner-Nordstr\"om-de Sitter black hole must always be unstable quantum mechanically.Comment: 4 pages; uses ReVTeX; figure available upon request to [email protected]

An approximate binary-black-hole metric

An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric is presented in a single coordinate system valid up to the apparent horizons of the black holes. This metric could be useful in numerical simulations of binary black holes. Initial data extracted from this metric have the advantages of being linked to the early inspiral phase of the binary system, and of not containing spurious gravitational waves.Comment: 20 pages, 1 figure; some changes in Sec. IV B,C and Sec.

On isotropic cylindrically symmetric stellar models

We attempt to match the most general cylindrically symmetric vacuum space-time with a Robertson-Walker interior. The matching conditions show that the interior must be dust filled and that the boundary must be comoving. Further, we show that the vacuum region must be polarized. Imposing the condition that there are no trapped cylinders on an initial time slice, we can apply a result of Thorne's and show that trapped cylinders never evolve. This results in a simplified line element which we prove to be incompatible with the dust interior. This result demonstrates the impossibility of the existence of an isotropic cylindrically symmetric star (or even a star which has a cylindrically symmetric portion). We investigate the problem from a different perspective by looking at the expansion scalars of invariant null geodesic congruences and, applying to the cylindrical case, the result that the product of the signs of the expansion scalars must be continuous across the boundary. The result may also be understood in relation to recent results about the impossibility of the static axially symmetric analogue of the Einstein-Straus model.Comment: 13 pages. To appear in Classical and Quantum Gravit