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

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.

Differential Forms and Wave Equations for General Relativity

Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and York (AACY) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equation in a system, describes vacuum general relativity. Whereas the approach of AACY is based on tensor-index methods, the present formulation is written solely in the language of differential forms. Our approach starts with Sparling's tetrad-dependent differential forms, and our wave equation governs the propagation of Sparling's 2-form, which in the ``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The tensor-index version of our wave equation describes the propagation of (what is essentially) the Arnowitt-Deser-Misner gravitational momentum.Comment: REVTeX, 26 pages, no figures, 1 macr

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

Theory and astrophysical consequences of a magnetized torus around a rapidly rotating black hole

(Abbrev.) We analyze the topology, lifetime, and emissions of a torus around a black hole formed in hypernovae and black hole-neutron star coalescence. The torus is ab initio uniformly magnetized, represented by two counter oriented current-rings, and develops a state of suspended accretion against a "magnetic wall" around the black hole. Magnetic stability of the torus gives rise to a new fundamental limit EB/Ek<0.1 for the ratio of poloidal magnetic field energy-to-kinetic energy. The lifetime of rapid spin of the black hole is effectively defined by the timescale of dissipation of black hole-spin energy in the horizon, and satisfies T= 40s (MH/7MSun)(R/6MH)^4(0.03MH/MT) for a black hole of mass MH surrounded by a torus of mass MT and radius R. The torus converts a major fraction Egw/Erot=0.1 into gravitational radiation through a finite number of multipole mass-moments, and a smaller fraction into MeV neutrinos and baryon-rich winds. At a source distance of 100Mpc, these emissions over N=2e4 periods give rise to a characteristic strain amplitude \sqrt{N}hchar=6e-21. We argue that torus winds create an open magnetic flux-tube on the black hole, which carries a minor and standard fraction Ej/Erot=1e-3 in baryon-poor outflows to infinity. We identify this baryon poor output of tens of seconds with GRBs with contemporaneous and strongly correlated emissions in gravitational radiation, conceivably at multiple frequencies. Ultimately, this leaves a black hole binary surrounded by a supernova remnant.Comment: To appear in ApJ (44p

Vitamin K status and physical decline in older adults—The Longitudinal Aging Study Amsterdam

Objective: We examined the association between vitamin K status and physical functioning over 13 years in the Longitudinal Aging Study Amsterdam. Study design: Longitudinal cohort study of 633 community-dwelling adults from the Longitudinal Aging Study Amsterdam (LASA) aged 55–65 years (54% women). Main outcome measures: At baseline (2002–2003), plasma desphospho-uncarboxylated matrix Gla protein (dp-ucMGP) was measured with a sandwich ELISA as a marker of vitamin K status. The outcome measures handgrip strength, calf circumference, self-reported functional limitations and functional performance were obtained at baseline and four follow-up examinations. We used generalized estimating equations to determine the relationship between dp-ucMGP tertiles and the various outcome measurements after adjusting for potential confounders. The lowest dp-ucMGP tertile reflects a high vitamin K status and was the reference. Results: Mean dp-ucMGP was 376 ± 233 pmol/L and mean follow-up was 11.1 years. Participants showed a decline in the outcome measures over time. Compared with the lowest tertile, the highest dp-ucMGP tertile had: lower handgrip strength, 1.1 kg (95% confidence interval (−2.1, −0.1; P-trend <0.001); smaller calf circumference, −0.5 cm (−0.9 −0.1; P-trend = 0.018); and, only among women, a 0.7-point poorer functional performance score (−1.1, −0.3; P-interaction = 0.002). Dp-ucMGP was not related to self-reported functional limitations. No interaction effects between time and dp-ucMGP were observed. Conclusions: Low vitamin K status was associated with lower handgrip strength, smaller calf circumference, and, in women only, with poorer functional performance score. A low vitamin K status was however not related to the 13-year decline in these measures

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

Determining geophysical responses from burials in graveyards and cemeteries

Graveyards and cemeteries around the world are increasingly designated as full. Therefore, there is a requirement to identify vacant spaces for new burials or to identify existing ones to exhume and then reinter if necessary. Geophysical methods offer a potentially noninvasive target detection solution; however, there has been limited research to identify optimal geophysical detection methods against burial age. We have collected multifrequency (225–900 MHz) ground-penetrating radar (GPR), electrical resistivity, and magnetic susceptibility surface data over known graves with different burial ages and soil types in three UK church graveyards. Results indicate that progressively older burials are more difficult to detect, but this decrease is not linear and is site specific. Medium- to high-frequency GPR and magnetic susceptibility was optimal in clay-rich soils, medium- to high-frequency GPR and electrical resistivity in sandy soils, and electrical resistivity and low-frequency GPR in coarse sand and pebbly soils, respectively. A multigeophysical technique approach should be used by survey practitioners where grave locations are not known to maximize target detection success. Grave soil and grave cuts are important grave position indicators. Grave headstones were not always located where burials were located. We have determined the value of these techniques in grave detection and could potentially date burials from their geophysical responses