Near-Constant Mean Curvature Solutions of the Einstein Constraint Equations with Non-Negative Yamabe Metrics

We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the Einstein constraint equations. This result extends previous work which required the conformal metric to be in the negative Yamabe class, and required the mean curvature function to be nonzero.Comment: 15 page

Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations

We describe how the iterative technique used by Isenberg and Moncrief to verify the existence of large sets of non constant mean curvature solutions of the Einstein constraints on closed manifolds can be adapted to verify the existence of large sets of asymptotically hyperbolic non constant mean curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure

Energy Conversion Alternatives Study (ECAS), Westinghouse phase 1. Volume 12: Fuel cells

A parametric assessment of four fuel cell power systems -- based on phosphoric acid, potassium hydroxide, molten carbonate, and stabilized zirconia -- has shown that the most important parameters for electricity-cost reduction and/or efficiency improvement standpoints are fuel cell useful life and power density, use of a waste-heat recovery system, and fuel type. Typical capital costs, overall energy efficiencies (based on the heating value of the coal used to produce the power plant fuel), and electricity costs are: phosphoric acid $350-450/kWe, 24-29$450-700/kWe, 26-31%, and 12.8 to 16.9 mills/MJ (46 to 61 mills/kWh); molten carbonate $480-650/kWe, 32-46$420-950/kWe, 26-53%, and 9.7 to 16.9 mills/MJ (35 to 61 mills/kWh). Three types of fuel cell power plants -- solid electrolytic with steam bottoming, molten carbonate with steam bottoming, and solid electrolyte with an integrated coal gasifier -- are recommended for further study

The constraint equations for the Einstein-scalar field system on compact manifolds

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.Comment: Minor changes, final version. To appear: Classical and Quantum Gravit

Cosmological spacetimes not covered by a constant mean curvature slicing

We show that there exist maximal globally hyperbolic solutions of the Einstein-dust equations which admit a constant mean curvature Cauchy surface, but are not covered by a constant mean curvature foliation.Comment: 11 page

Canonical Quantization Inside the Schwarzschild Black Hole

We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition. For the interior we appeal to the need for CPT invariance to construct an explicitly positive definite operator which allows identification of positive and negative frequencies. This operator is the translation operator corresponding to the inexorable propagation to smaller radii as expected from the classical metric. We also propose an expression for the propagator in the interior and express it as a mode sum.Comment: 8 pages, LaTex. Title altered. One reference added. A few typos esp. eq.(7),(38) corrected. To appear in Class.Q.Gra

Testing Approximations of Thermal Effects in Neutron Star Merger Simulations

We perform three-dimensional relativistic hydrodynamical calculations of neutron star mergers to assess the reliability of an approximate treatment of thermal effects in such simulations by combining an ideal-gas component with zero-temperature, micro-physical equations of state. To this end we compare the results of simulations that make this approximation to the outcome of models with a consistent treatment of thermal effects in the equation of state. In particular we focus on the implications for observable consequences of merger events like the gravitational-wave signal. It is found that the characteristic gravitational-wave oscillation frequencies of the post-merger remnant differ by about 50 to 250 Hz (corresponding to frequency shifts of 2 to 8 per cent) depending on the equation of state and the choice of the characteristic index of the ideal-gas component. In addition, the delay time to black hole collapse of the merger remnant as well as the amount of matter remaining outside the black hole after its formation are sensitive to the description of thermal effects.Comment: 10 pages, 6 figures, 9 eps files; revised with minor additions due to referee comments; accepted by Phys.Rev.

Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

Analysis of the relationship between disease activity and damage in patients with systemic lupus erythematosus—a 5-yr prospective study

Objective. To determine whether initial damage, disease duration, age, initial health status, average disease activity over the 5 yr or an average medication score covering the follow-up period would predict an increase in damage in patients with systemic lupus erythematosus (SLE) within the next 5 yr. Methods. A 5-yr prospective longitudinal study of a cohort of 141 consecutive patients with SLE attending a specialist lupus out-patient clinic in London from their first assessment between July 1994 and February 1995. Disease activity was assessed using the BILAG system, initial health status by the Medical Outcome Survey Short Form 20 with an extra question about fatigue (SF-20+) and damage by the SLICC/ACR Damage Index (SDI). Damage was reassessed 5 yr later. Statistical analysis was carried out using multiple logistic regression analysis (logXact). Results. One hundred and thirty-three female and eight male SLE patients (97 Caucasians, 16 Afro-Caribbeans, 22 Asians and 6 others) were included, their age at inclusion was 41.1 ± 12.5 yr and their disease duration 10.2 ± 6.3 yr. The mean measures at inclusion were: total BILAG 5.2 (range 0-17), total SDI 1.2 (0-7) and medication score 1.2 (0-3). Six patients were lost to follow-up because they had moved. Of the remaining 135 patients total damage had increased in 40 patients and 10 patients had died. At the end of the study, at 4.63 ± 0.19 yr, the total SDI had increased to 1.6 ± 1.7. Multiple logistic regression analysis revealed that death and increase in damage were strongly predicted by a high total disease activity over the entire study period (P<0.001) as we had hypothesized. When the total BILAG score was replaced by the average number of A-flares the prediction of accrual of damage during the study period was again highly significant (P = 0.004). Conclusions. In this first prospective study of its type a highly significant impact of total disease activity, as measured over 5 yr using the BILAG system, on the development of total damage was revealed. Moreover, these results provide further proof of the validity of the SDI and support the BILAG concept of the A-flare

Non-conformally flat initial data for binary compact objects

A new method is described for constructing initial data for a binary neutron-star (BNS) system in quasi-equilibrium circular orbit. Two formulations for non-conformally flat data, waveless (WL) and near-zone helically symmetric (NHS), are introduced; in each formulation, the Einstein-Euler system, written in 3+1 form on an asymptotically flat spacelike hypersurface, is exactly solved for all metric components, including the spatially non-conformally flat potentials, and for irrotational flow. A numerical method applicable to both formulations is explained with an emphasis on the imposition of a spatial gauge condition. Results are shown for solution sequences of irrotational BNS with matter approximated by parametrized equations of state that use a few segments of polytropic equations of state. The binding energy and total angular momentum of solution sequences computed within the conformally flat -- Isenberg-Wilson-Mathews (IWM) -- formulation are closer to those of the third post-Newtonian (3PN) two point particles up to the closest orbits, for the more compact stars, whereas sequences resulting from the WL/NHS formulations deviate from the 3PN curve even more for the sequences with larger compactness. We think it likely that this correction reflects an overestimation in the IWM formulation as well as in the 3PN formula, by $\sim 1$ cycle in the gravitational wave phase during the last several orbits. The work suggests that imposing spatial conformal flatness results in an underestimate of the quadrupole deformation of the components of binary neutron-star systems in the last few orbits prior to merger.Comment: 22 pages, 7 figure