Oscillations of Thick Accretion Discs Around Black Holes

We present a numerical study of the response of a thick accretion disc to a localized, external perturbation with the aim of exciting internal modes of oscillation. We find that the perturbations efficiently excite global modes recently identified as acoustic p--modes, and closely related to the epicyclic oscillations of test particles. The two strongest modes occur at eigenfrequencies which are in a 3:2 ratio. We have assumed a constant specific angular momentum distribution within the disc. Our models are in principle scale--free and can be used to simulate accretion tori around stellar or super massive black holes.Comment: 4 pages, 4 figures, accepted for publication as a letter in the Monthly Notices of the Royal Astronomical Societ

Oscillations of Thick Accretion Discs Around Black Holes - II

We present a numerical study of the global modes of oscillation of thick accretion discs around black holes. We have previously studied the case of constant distributions of specific angular momentum. In this second paper, we investigate (i) how the size of the disc affects the oscillation eigenfrequencies, and (ii) the effect of power-law distributions of angular momentum on the oscillations. In particular, we compare the oscillations of the disc with the epicyclic eigenfrequencies of a test particle with different angular momentum distributions orbiting around the central object. We find that there is a frequency shift away from the epicyclic eigenfrequency of the test particle to lower values as the size of the tori is increased. We have also studied the response of a thick accretion disc to a localized external perturbation using non constant specific angular momentum distributions within the disc. We find that in this case it is also possible (as reported previously for constant angular momentum distributions) to efficiently excite internal modes of oscillation. In fact we show here that the local perturbations excite global oscillations (acoustic p modes) closely related to the epicyclic oscillations of test particles. Our results are particularly relevant in the context of low mass X-ray binaries and microquasars, and the high frequency Quasi-Periodic Oscillations (QPOs) observed in them. Our computations make use of a Smooth Particle Hydrodynamics (SPH) code in azimuthal symmetry, and use a gravitational potential that mimics the effects of strong gravity.Comment: 10 pages, 8 figures, accepted for publication as a paper in the Monthly Notices of the Royal Astronomical Societ

Past and future gauge in numerical relativity

Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of present time. Here, we propose solving the discretized Einstein equations with a choice of gauge in the future and a dynamical gauge in the past. The method is illustrated on a polarized Gowdy wave.Comment: To appear in Class Quantum Grav, Let

Scattering Lens Resolves sub-100 nm Structures with Visible Light

The smallest structures that conventional lenses are able to optically resolve are of the order of 200 nm. We introduce a new type of lens that exploits multiple scattering of light to generate a scanning nano-sized optical focus. With an experimental realization of this lens in gallium phosphide we have succeeded to image gold nanoparticles at 97 nm optical resolution. Our work is the first lens that provides a resolution in the nanometer regime at visible wavelengths.Comment: 4 pages, 3 figure

Gravitational radiation from gamma-ray bursts as observational opportunities for LIGO and VIRGO

Gamma-ray bursts are believed to originate in core-collapse of massive stars. This produces an active nucleus containing a rapidly rotating Kerr black hole surrounded by a uniformly magnetized torus represented by two counter-oriented current rings. We quantify black hole spin-interactions with the torus and charged particles along open magnetic flux-tubes subtended by the event horizon. A major output of Egw=4e53 erg is radiated in gravitational waves of frequency fgw=500 Hz by a quadrupole mass-moment in the torus. Consistent with GRB-SNe, we find (i) Ts=90s (tens of s, Kouveliotou et al. 1993), (ii) aspherical SNe of kinetic energy Esn=2e51 erg (2e51 erg in SN1998bw, Hoeflich et al. 1999) and (iii) GRB-energies Egamma=2e50 erg (3e50erg in Frail et al. 2001). GRB-SNe occur perhaps about once a year within D=100Mpc. Correlating LIGO/Virgo detectors enables searches for nearby events and their spectral closure density 6e-9 around 250Hz in the stochastic background radiation in gravitational waves. At current sensitivity, LIGO-Hanford may place an upper bound around 150MSolar in GRB030329. Detection of Egw thus provides a method for identifying Kerr black holes by calorimetry.Comment: to appear in PRD, 49

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.

On the detectability of gravitational waves background produced by gamma ray bursts

In this paper we discuss a new strategy for the detection of gravitational radiation likely emitted by cosmological gamma ray burst. Robust and conservative estimates lead to the conclusion that the uncorrelated superimposition of bursts of gravitational waves can be detected by interferometric detectors like VIRGO or LIGO. The expected signal is predicted to carry two very distinctive signatures: the cosmological dipole anisotropy and a characteristic time scale in the auto correlation spectrum, which might be exploited, perhaps with ad hoc modifications and/or upgrading of the planned experiments, to confirm the non-instrumental origin of the signal.Comment: 9 pages, 2 figures, LATEX2e, Accepted for pubblications as a Letter to the Editor in Journal of Physics G: Nuclear and Particle Physic

Optimal Concentration of Light in Turbid Materials

In turbid materials it is impossible to concentrate light into a focus with conventional optics. Recently it has been shown that the intensity on a dyed probe inside a turbid material can be enhanced by spatially shaping the wave front of light before it enters a turbid medium. Here we show that this enhancement is due to concentration of light energy to a spot much smaller than a wavelength. We focus light on a dyed probe sphere that is hidden under an opaque layer. The light is optimally concentrated to a focus which does not exceed the smallest focal area physically possible by more than 68%. A comparison between the intensity enhancements of both the emission and excitation light supports the conclusion of optimal light concentration.Comment: We corrected an ambiguous description of the focus size in our abstract and text pointed out by an anonymous refere

Electron-Positron Jets from a Critically Magnetized Black Hole

The curved spacetime surrounding a rotating black hole dramatically alters the structure of nearby electromagnetic fields. The Wald field which is an asymptotically uniform magnetic field aligned with the angular momentum of the hole provides a convenient starting point to analyze the effects of radiative corrections on electrodynamics in curved spacetime. Since the curvature of the spacetime is small on the scale of the electron's Compton wavelength, the tools of quantum field theory in flat spacetime are reliable and show that a rotating black hole immersed in a magnetic field approaching the quantum critical value of $B_k=m^2 c^3/(e\hbar) \approx 4.4 \times 10^{13}$~G $\approx 1.3\times10^{-11}$ cm$^{-1}$ is unstable. Specifically, a maximally rotating three-solar-mass black hole immersed in a magnetic field of $2.3 \times 10^{12}$~G would be a copious producer of electron-positron pairs with a luminosity of $3 \times 10^{52}$ erg s$^{-1}$.Comment: 10 pages, 6 figures, submitted to Phys. Rev.

Nonlinear DC-response in Composites: a Percolative Study

The DC-response, namely the $I$-$V$ and $G$-$V$ charateristics, of a variety of composite materials are in general found to be nonlinear. We attempt to understand the generic nature of the response charactersistics and study the peculiarities associated with them. Our approach is based on a simple and minimal model bond percolative network. We do simulate the resistor network with appropritate linear and nonlinear bonds and obtain macroscopic nonlinear response characteristics. We discuss the associated physics. An effective medium approximation (EMA) of the corresponding resistor network is also given.Comment: Text written in RevTEX, 15 pages (20 postscript figures included), submitted to Phys. Rev. E. Some minor corrections made in the text, corrected one reference, the format changed (from 32 pages preprint to 15 pages