Numerical Integration of Nonlinear Wave Equations for General Relativity

A second-order numerical implementation is given for recently derived nonlinear wave equations for general relativity. The Gowdy T$^3$ cosmology is used as a test bed for studying the accuracy and convergence of simulations of one-dimensional nonlinear waves. The complete freedom in space-time slicing in the present formulation is exploited to compute in the Gowdy line-element. Second-order convergence is found by direct comparison of the results with either analytical solutions for polarized waves, or solutions obtained from Gowdy's reduced wave equations for the more general unpolarized waves. Some directions for extensions are discussed.Comment: 19 pages (LaTex), 3 figures (ps

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

Electric Charge and Magnetic Flux on Rotating Black Holes in a Force-Free Magnetosphere

The electric charge on rotating black holes is calculated to be ~ BJ in the force-free configuration of Ghosh (2000), with a horizon flux of ~ BM^2. This charge is gravitationally weak for B ~ 10^{15} G, so that the Kerr metric applies. Being similar to the electric charge of a magnetar, both electric charge and magnetic flux should be, in sign and order of magnitude, continuous during stellar collapse into a black hole. Extraction of the rotational energy from newly formed black holes may proceed by interaction with the magnetic field. Keywords:black hole physics --magnetic fieldsComment: 11 pages, no figure, restructured with sections and revisions in abstarct and in the text, version accepted for MNRA

Uniqueness in MHD in divergence form: right nullvectors and well-posedness

Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of well-posedness, and identify a preferred linear combination in this divergence formulation. The limit of weak magnetic fields shows the slow magnetosonic and Alfven waves to bifurcate from the contact discontinuity (entropy waves), while the fast magnetosonic wave is a regular perturbation of the hydrodynamical sound speed. These results are further reported as a starting point for characteristic based shock capturing schemes for simulations with ultra-relativistic shocks in magnetized relativistic fluids.Comment: To appear in J Math Phy

Gravitational wave frequencies and energies in hypernovae

A torus develops a state of suspended accretion against a magnetic wall around a rapidly rotating black hole formed in core-collapse hypernovae. It hereby emits about 10% of the black hole spin-energy in gravitational radiation from a finite number of multipole mass moments. We quantify the relation between the frequency of quadrupole gravitational radiation and the energy output $E_w$ in torus winds by $f_{gw}\simeq 470{Hz}(E_w/4\times 10^{52}{erg})^{1/2}(7M_\odot/M)^{3/2}$, where $M$ denotes the mass of the black hole. We propose that $E_w$ irradiates the remnant stellar envelope from within. We identify $E_w$ with energies $\sim 10^{52}$ erg inferred from X-ray observations on matter injecta; and the poloidal curvature in the magnetic wall with the horizon opening angle in baryon poor outflows that power true GRB energies of $E_\gamma\simeq 3\times 10^{51}$ erg.Comment: To appear in AP

Non-thermal transient sources from rotating black holes

Rotating black holes can power the most extreme non-thermal transient sources. They have a long-duration viscous time-scale of spin-down and produce non-thermal emissions along their spin-axis, powered by a relativistic capillary effect. We report on the discovery of exponential decay in BATSE light curves of long GRBs by matched filtering, consistent with a viscous time-scale, and identify UHECRs energies about the GZK threshold in linear acceleration of ion contaminants along the black hole spin-axis, consistent with black hole masses and lifetimes of FR II AGN. We explain the absence of UHECRs from BL Lac objects due to UHECR emissions preferably at appreciable angles away from the black hole spin-axis. Black hole spin may be key to unification of GRBs and their host environments, and to AGN and their host galaxies. Our model points to long duration bursts in radio from long GRBs without supernovae and gravitational-waves from all long GRBs.Comment: Accepted by MNRA

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

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

Measurement of the ΔS=-ΔQ Amplitude from K_(e3)^0 Decay

We have measured the time distribution of the π^+e^-ν and π^-e^+ν modes from initial K^0's in a spark-chamber experiment performed at the Bevatron. From 1079 events between 0.2 and 7 K_S^0 lifetime, we find ReX=-0.069±0.036, ImX=+0.108_(-0.074)^(+0.092). This result is consistent with X=0 (relative probability = 0.25), but more than 4 standard deviations from the existing world average, +0.14 -0.13i

Возможностим развития конкуренции на рынках теплоснабжения Донбасса

Проаналізовано стан ситем теплопостачання Донбасу, виявлено зниження виробництва та відпуску теплової енергії, що викликано появою конкурента — автономного опалення. Обгрунтовано причини протиріччя законодавства, що регулює діяльність у сфері комунального теплопостачання — природної монополії, в результаті чого порушені конституційні, цивільні, споживчі права людей. Розглянуто практику регулювання ринків теплопостачання в країнах з розвиненою ринковою економікою, і можливості застосування їх досвіду в Україні. Визначено роль держави, як найважливішого регулятора, який здійснює контроль за ринком теплопостачання, і є влавником стратегічно важливих підприємств сектора. Ключові слова: централізоване теплопостачання, природна монополія, автономне опалення, конкуренція, приватний капітал, державне регулювання.Проанализировано состояние ситем теплоснабжения Донбасса, выявлено снижение производства и отпуска тепловой энергии, что вызвано появлением конкурента — автономного отопления. Обоснованы причины протеворечивости законодательства регулирующего деятельность в сфере коммунального теплоснабжения — естественной монополии, в результате чего нарушены конституционные, гражданские, потребительские права людей. Рассмотрена практика регулирования рынков теплоснабжения в странах с развитой рыночной экономикой, и возможности применения их опыта в Украине. Определена роль государства, как важнейшего регулятора, осуществляющего контроль за рынком теплоснабжения, и собственика стратегически важных предприятий сектора. Ключевые слова: централизованное теплоснабжение, естественная монополия, автономное отопление, конкуренция, частный капитал, государственное регулирование.The state of Donbass Heating System Works, showed a reduction in production and supply of heat energy that is caused by the emergence of competitors — independent heating. Substantiated reasons imperfect legislation governing activities in the field of district heating — natural monopoly, resulting in a violation of the constitutional, civil, consumer rights of people. The practical management of district heating markets in countries with developed market economies, and the possibility of applying their experience in Ukraine. Defined the place of government as an important regulator, controlling the heating market, and the owners of strategically important enterprises in the sector. Key words: district heating, natural monopoly, independent heating, competition, private capital, government regulation