27,045 research outputs found
Testing a Simplified Version of Einstein's Equations for Numerical Relativity
Solving dynamical problems in general relativity requires the full machinery
of numerical relativity. Wilson has proposed a simpler but approximate scheme
for systems near equilibrium, like binary neutron stars. We test the scheme on
isolated, rapidly rotating, relativistic stars. Since these objects are in
equilibrium, it is crucial that the approximation work well if we are to
believe its predictions for more complicated systems like binaries. Our results
are very encouraging.Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-107
Quasi-circular Orbits for Spinning Binary Black Holes
Using an effective potential method we examine binary black holes where the
individual holes carry spin. We trace out sequences of quasi-circular orbits
and locate the innermost stable circular orbit as a function of spin. At large
separations, the sequences of quasi-circular orbits match well with
post-Newtonian expansions, although a clear signature of the simplifying
assumption of conformal flatness is seen. The position of the ISCO is found to
be strongly dependent on the magnitude of the spin on each black hole. At close
separations of the holes, the effective potential method breaks down. In all
cases where an ISCO could be determined, we found that an apparent horizon
encompassing both holes forms for separations well inside the ISCO.
Nevertheless, we argue that the formation of a common horizon is still
associated with the breakdown of the effective potential method.Comment: 13 pages, 10 figures, submitted to PR
Towards a wave-extraction method for numerical relativity. V. Extracting the Weyl scalars in the quasi-Kinnersley tetrad from spatial data
We extract the Weyl scalars and in the quasi-Kinnersley
tetrad by finding initially the (gauge--, tetrad--, and
background--independent) transverse quasi-Kinnersley frame. This step still
leaves two undetermined degrees of freedom: the ratio , and
one of the phases (the product and the {\em sum} of
the phases are determined by the so-called BB radiation scalar). The residual
symmetry ("spin/boost") can be removed by gauge fixing of spin coefficients in
two steps: First, we break the boost symmetry by requiring that
corresponds to a global constant mass parameter that equals the ADM mass (or,
equivalently in perturbation theory, that or equal their values in
the no-radiation limits), thus determining the two moduli of the Weyl scalars
, while leaving their phases as yet undetermined. Second,
we break the spin symmetry by requiring that the ratio gives the
expected polarization state for the gravitational waves, thus determining the
phases. Our method of gauge fixing--specifically its second step--is
appropriate for cases for which the Weyl curvature is purely electric. Applying
this method to Misner and Brill--Lindquist data, we explicitly find the Weyl
scalars and perturbatively in the quasi-Kinnersley tetrad.Comment: 13 page
Predictions for the fracture toughness of cancellous bone of fracture neck of femur patients
Current protocol in determining if a patient is osteoporotic and their fracture risk is based on dual energy X-ray absorptiometry (DXA). DXA gives an indication of their bone mineral density (BMD) which is the product of both the porosity and density of the mineralized bone tissue; this is usually taken at the hip. The DXA results are assessed using the fracture risk assessment tool as recommended by the World Health Organization. While this provides valuable data on a person’s fracture risk advancements in medical imagining technology enables development of more robust and accurate risk assessment tools. In order to develop such tools in vitro analysis of bone is required to assess the morphological properties of bone osteoporotic bone tissue and how these pertain to the fracture toughness (Kcmax) of the tissue.Support was provided by the EPSRC (EP/K020196: Point-ofCare High Accuracy Fracture Risk Prediction), the UK Department of Transport under the BOSCOS (Bone Scanning for Occupant Safety) project, and approved by Gloucester and Cheltenham NHS Trust hospitals under ethical consent (BOSCOS – Mr. Curwen CI REC ref 01/179G)
Relativistic stars in differential rotation: bounds on the dragging rate and on the rotational energy
For general relativistic equilibrium stellar models (stationary axisymmetric
asymptotically flat and convection-free) with differential rotation, it is
shown that for a wide class of rotation laws the distribution of angular
velocity of the fluid has a sign, say "positive", and then both the dragging
rate and the angular momentum density are positive. In addition, the "mean
value" (with respect to an intrinsic density) of the dragging rate is shown to
be less than the mean value of the fluid angular velocity (in full general,
without having to restrict the rotation law, nor the uniformity in sign of the
fluid angular velocity); this inequality yields the positivity and an upper
bound of the total rotational energy.Comment: 23 pages, no figures, LaTeX. Submitted to J. Math. Phy
Inner boundary conditions for black hole Initial Data derived from Isolated Horizons
We present a set of boundary conditions for solving the elliptic equations in
the Initial Data Problem for space-times containing a black hole, together with
a number of constraints to be satisfied by the otherwise freely specifiable
standard parameters of the Conformal Thin Sandwich formulation. These
conditions altogether are sufficient for the construction of a horizon that is
instantaneously in equilibrium in the sense of the Isolated Horizons formalism.
We then investigate the application of these conditions to the Initial Data
Problem of binary black holes and discuss the relation of our analysis with
other proposals that exist in the literature.Comment: 13 pages. Major general revision. Section V comparing with previous
approaches restructured; discussion on the lapse boundary condition extended.
Appendix with some technical details added. Version accepted for publication
in Phys.Rev.
Alternatives to standard puncture initial data for binary black hole evolution
Standard puncture initial data have been widely used for numerical binary
black hole evolutions despite their shortcomings, most notably the inherent
lack of gravitational radiation at the initial time that is later followed by a
burst of spurious radiation. We study the evolution of three alternative
initial data schemes. Two of the three alternatives are based on post-Newtonian
expansions that contain realistic gravitational waves. The first scheme is
based on a second-order post-Newtonian expansion in Arnowitt, Deser, and Misner
transverse-traceless (ADMTT) gauge that has been resummed to approach standard
puncture data at the black holes. The second scheme is based on asymptotic
matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to a
first-order post-Newtonian expansion in ADMTT gauge away from the black holes.
The final alternative is obtained through asymptotic matching of the 4-metrics
of two tidally perturbed Schwarzschild solutions to a second-order
post-Newtonian expansion in harmonic gauge away from the black holes. When
evolved, the second scheme fails to produce quasicircular orbits (and instead
leads to a nearly head-on collision). This failure can be traced back to
inaccuracies in the extrinsic curvature due to low order matching. More
encouraging is that the latter two alternatives lead to quasicircular orbits
and show gravitational radiation from the onset of the evolution, as well as a
reduction of spurious radiation. Current deficiencies compared to standard
punctures data include more eccentric trajectories during the inspiral and
larger constraint violations, since the alternative data sets are only
approximate solutions of Einstein's equations. The eccentricity problem can be
ameliorated by adjusting the initial momentum parameters.Comment: 11 pages, 11 figures, 1 appendix, typos corrected, removed duplicate
reference, matches published versio
Evolution of Binary Black Hole Spacetimes
We describe early success in the evolution of binary black hole spacetimes
with a numerical code based on a generalization of harmonic coordinates.
Indications are that with sufficient resolution this scheme is capable of
evolving binary systems for enough time to extract information about the orbit,
merger and gravitational waves emitted during the event. As an example we show
results from the evolution of a binary composed of two equal mass, non-spinning
black holes, through a single plunge-orbit, merger and ring down. The resultant
black hole is estimated to be a Kerr black hole with angular momentum parameter
a~0.70. At present, lack of resolution far from the binary prevents an accurate
estimate of the energy emitted, though a rough calculation suggests on the
order of 5% of the initial rest mass of the system is radiated as gravitational
waves during the final orbit and ringdown.Comment: 4 pages, 3 figure
Design and development of a water vapor electrolysis unit
Design and development of water vapor electrolysis unit for oxygen productio
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