2,107 research outputs found
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 ÎS=-ÎQ Amplitude from K_(e3)^0 Decay
We have measured the time distribution of the Ï^+e^-Îœ and Ï^-e^+Îœ 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
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
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 (225â900Â 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
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
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