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 $\Psi_0$ and $\Psi_4$ 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 $|\Psi_0|/|\Psi_4|$, and one of the phases (the product $|\Psi_0|\cdot |\Psi_4|$ 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 $\rho$ corresponds to a global constant mass parameter that equals the ADM mass (or, equivalently in perturbation theory, that $\rho$ or $\mu$ equal their values in the no-radiation limits), thus determining the two moduli of the Weyl scalars $|\Psi_0|, |\Psi_4|$, while leaving their phases as yet undetermined. Second, we break the spin symmetry by requiring that the ratio $\pi/\tau$ 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 $\Psi_0$ and $\Psi_4$ 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.

Design and development of a water vapor electrolysis unit

Design and development of water vapor electrolysis unit for oxygen productio

Quasi-equilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions

We construct a sequence of binary black hole puncture data derived under the assumptions (i) that the ADM mass of each puncture as measured in the asymptotically flat space at the puncture stays constant along the sequence, and (ii) that the orbits along the sequence are quasi-circular in the sense that several necessary conditions for the existence of a helical Killing vector are satisfied. These conditions are equality of ADM and Komar mass at infinity and equality of the ADM and a rescaled Komar mass at each puncture. In this paper we explicitly give results for the case of an equal mass black hole binary without spin, but our approach can also be applied in the general case. We find that up to numerical accuracy the apparent horizon mass also remains constant along the sequence and that the prediction for the innermost stable circular orbit is similar to what has been found with the effective potential method.Comment: 6 pages, 3 figures, 1 tabl

High-precision radiocarbon dating of the construction phase of Oakbank Crannog, Loch Tay, Perthshire

Many of the Loch Tay crannogs were built in the Early Iron Age and so calibration of the radiocarbon ages produces very broad calendar age ranges due to the well-documented Hallstatt plateau in the calibration curve. However, the large oak timbers that were used in the construction of some of the crannogs potentially provide a means of improving the precision of the dating through subdividing them into decadal or subdecadal increments, dating them to high precision and wiggle-matching the resulting data to the master <sup>14</sup>C calibration curve. We obtained a sample from 1 oak timber from Oakbank Crannog comprising 70 rings (Sample OB06 WMS 1, T103) including sapwood that was complete to the bark edge. The timber is situated on the northeast edge of the main living area of the crannog and as a large and strong oak pile would have been a useful support in more than 1 phase of occupation and may be related to the earliest construction phase of the site. This was sectioned into 5-yr increments and dated to a precision of approximately ±8–16 <sup>14</sup>C yr (1 σ). The wiggle-match predicts that the last ring dated was formed around 500 BC (maximum range of 520–465 BC) and should be taken as indicative of the likely time of construction of Oakbank Crannog. This is a considerable improvement on the estimates based on single <sup>14</sup>C ages made on oak samples, which typically encompassed the period from around 800–400 BC

Gravitational waves from nonspinning black hole-neutron star binaries: dependence on equations of state

We report results of a numerical-relativity simulation for the merger of a black hole-neutron star binary with a variety of equations of state (EOSs) modeled by piecewise polytropes. We focus in particular on the dependence of the gravitational waveform at the merger stage on the EOSs. The initial conditions are computed in the moving-puncture framework, assuming that the black hole is nonspinning and the neutron star has an irrotational velocity field. For a small mass ratio of the binaries (e.g., MBH/MNS = 2 where MBH and MNS are the masses of the black hole and neutron star, respectively), the neutron star is tidally disrupted before it is swallowed by the black hole irrespective of the EOS. Especially for less-compact neutron stars, the tidal disruption occurs at a more distant orbit. The tidal disruption is reflected in a cutoff frequency of the gravitational-wave spectrum, above which the spectrum amplitude exponentially decreases. A clear relation is found between the cutoff frequency of the gravitational-wave spectrum and the compactness of the neutron star. This relation also depends weakly on the stiffness of the EOS in the core region of the neutron star, suggesting that not only the compactness but also the EOS at high density is reflected in gravitational waveforms. The mass of the disk formed after the merger shows a similar correlation with the EOS, whereas the spin of the remnant black hole depends primarily on the mass ratio of the binary, and only weakly on the EOS. Properties of the remnant disks are also analyzed.Comment: 27pages, 21 figures; erratum is added on Aug 5. 201