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

Calorimetry of gamma-ray bursts: echos in gravitational waves

Black holes surrounded by a disk or torus may drive the enigmatic cosmological gamma-ray bursts (GRBs). Equivalence in poloidal topology to pulsar magnetospheres shows a high incidence of the black hole-luminosity $L_H$ into the surrounding magnetized matter. We argue that this emission is re-radiated into gravitational waves at $L_{GW}\simeq L_H/3$ in frequencies of order 1kHz, winds and, potentially, MeV neutrinos. The total energy budget and input to the GRB from baryon poor jets are expected to be standard in this scenario, consistent with recent analysis of afterglow data. Collimation of these outflows by baryon rich disk or torus winds may account for the observed spread in opening angles up to about $35^o$. This model may be tested by future LIGO/VIRGO observations.Comment: To appear in ApJ

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

The Gowdy T3 Cosmologies revisited

We have examined, repeated and extended earlier numerical calculations of Berger and Moncrief for the evolution of unpolarized Gowdy T3 cosmological models. Our results are consistent with theirs and we support their claim that the models exhibit AVTD behaviour, even though spatial derivatives cannot be neglected. The behaviour of the curvature invariants and the formation of structure through evolution both backwards and forwards in time is discussed.Comment: 11 pages, LaTeX, 6 figures, results and conclusions revised and (considerably) expande

Hyper- and suspended-accretion states of rotating black holes and the durations of gamma-ray bursts

We analyze the temporal evolution of accretion onto rotating black holes subject to large-scale magnetic torques. Wind torques alone drive a disk towards collapse in a finite time $\sim t_{ff} E_k/E_B$, where $t_{ff}$ is the initial free-fall time and $E_k/E_B$ is the ratio of kinetic-to-poloidal magnetic energy. Additional spin-up torques from a rapidly rotating black hole can arrest the disk's inflow. We associate short/long gamma-ray bursts with hyperaccretion/suspended-accretion onto slowly/rapidly spinning black holes. This model predicts afterglow emission from short bursts, and may be tested by HETE-II.Comment: accepted for publication in the ApJ

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

Localization, Coulomb interactions and electrical heating in single-wall carbon nanotubes/polymer composites

Low field and high field transport properties of carbon nanotubes/polymer composites are investigated for different tube fractions. Above the percolation threshold f_c=0.33%, transport is due to hopping of localized charge carriers with a localization length xi=10-30 nm. Coulomb interactions associated with a soft gap Delta_CG=2.5 meV are present at low temperature close to f_c. We argue that it originates from the Coulomb charging energy effect which is partly screened by adjacent bundles. The high field conductivity is described within an electrical heating scheme. All the results suggest that using composites close to the percolation threshold may be a way to access intrinsic properties of the nanotubes by experiments at a macroscopic scale.Comment: 4 pages, 5 figures, Submitted to Phys. Rev.

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.

Electron-positron outflow from black holes

Gamma-ray bursts (GRBs) appear as the brightest transient phenomena in the Universe. The nature of the central engine in GRBs is a missing link in the theory of fireballs to their stellar mass progenitors. Here it is shown that rotating black holes produce electron-positron outflow when brought into contact with a strong magnetic field. The outflow is produced by a coupling of the spin of the black hole to the orbit of the particles. For a nearly extreme Kerr black hole, particle outflow from an initial state of electrostatic equilibrium has a normalized isotropic emission of $\sim 5\times10^{48}(B/B_c)^2(M/7M_\odot)^2\sin^2\theta$ erg/s, where B is the external magnetic field strength, B_c=4.4 x 10^{13}G, and M is the mass of the black hole. This initial outflow has a half-opening angle $\theta\ge\sqrt{B_c/3B}$. A connection with fireballs in $\gamma$-ray bursts is given.Comment: 10 pages LaTe

Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies

Heuristic arguments and numerical simulations support the Belinskii et al (BKL) claim that the approach to the singularity in generic gravitational collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By writing the metric of one spacetime in the standard variables of another, signatures for LMD may be found. Such signatures for the dynamics of spatially homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the dynamics of generic $T^2$-symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief