Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of the Einstein equations

We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously proposed "$\lambda$-system", which introduces artificial flows to constraint surfaces based on the symmetric hyperbolic formulation. We show that this system works as expected for the wave propagation problem in the Maxwell system and in general relativity using Ashtekar's connection formulation. Second, we propose a new mechanism to control the stability, which we call the ``adjusted system". This is simply obtained by adding constraint terms in the dynamical equations and adjusting its multipliers. We explain why a particular choice of multiplier reduces the numerical errors from non-positive or pure-imaginary eigenvalues of the adjusted constraint propagation equations. This ``adjusted system" is also tested in the Maxwell system and in the Ashtekar's system. This mechanism affects more than the system's symmetric hyperbolicity.Comment: 16 pages, RevTeX, 9 eps figures, added Appendix B and minor changes, to appear in Class. Quant. Gra

Non-equilibrium Studies in Switching Arc Plasmas in Japan

This paper briefly introduce research work examples of non-equilibrium studies in switching arcs. In understanding arc behavior, one often assumes local thermodynamic equilibrium (LTE) condition in the arc plasma. However, actual arc plasmas are not completely and not always in LTE state because of strong temperature change temporally and spatially, and high electric field application etc. Recently, we have a collaboration work in numerical simulations and experimental approaches for decaying arcs without LTE assumption. First, our numerical model is presented for decaying arcs without chemical equilibrium assumption. Secondly, two experimental methods are introduced for measuring electron density in decaying arcs without LTE assumption: Laser Thomson Scattering method and the Schack-Hartmann method. Finally, comparison results is shown between the LTE simulation, the chemically non-equilibrium simulation, and the above experimental measurements

Symmetric hyperbolic system in the Ashtekar formulation

We present a first-order symmetric hyperbolic system in the Ashtekar formulation of general relativity for vacuum spacetime. We add terms from constraint equations to the evolution equations with appropriate combinations, which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev. Lett. 79, 4732 (1997)]. However our system is different from theirs in the points that we primarily use Hermiticity of a characteristic matrix of the system to characterize our system "symmetric", discuss the consistency of this system with reality condition, and show the characteristic speeds of the system.Comment: 4 pages, RevTeX, to appear in Phys. Rev. Lett., Comments added, refs update

Risk for hepatocellular carcinoma with respect to hepatitis B virus genotypes B/C, specific mutations of enhancer II/core promoter/precore regions and HBV DNA levels

Background/aim: To examine the risks for hepatocellular carcinoma (HCC) with respect to hepatitis B virus (HBV) genotypes, specific viral mutations (MT), serum HBV DNA levels, and cirrhosis. Methods: HBV genotypes, 1653/1753/core promoter (CP)/precore MT and HBV DNA levels were determined in 248 HBV patients with HCC and 248 HBV controls. Results: Genotype C, CP-MT, T1653, HBV DNA levels ≥4 log 10 copies/ml and cirrhosis had a higher risk for HCC compared to patients with genotype B (p = 0.001, OR 1.9), CP wild-type (WT) (p<0.001, OR 4.1), C1653 (p = 0.028, OR 2.4), HBV DNA <4 log 10 copies/ml (p = 0.003, OR 2.1) and without cirrhosis (p<0.001, OR 4.0) respectively. Multivariate analysis showed that CP-MT, T1653, HBV DNA ≥4 log 10 copies/ml and cirrhosis were independent factors for HCC (all p<0.05). A receiver operating characteristics curve showed no cut-off HBV DNA level associated with minimal chance of HCC. Patients with CP-MT and cirrhosis had a 22.2-fold increased risk of HCC compared to patients with CP-WT and without cirrhosis. Patients with CP-MT and HBV DNA levels ≥4 log 10 copies/ml had a 7.2-fold increased risk of HCC compared to patients with CP-WT and HBV DNA levels <4 log 10 copies/ml. Patients with CP-MT and T1653 had a 9.9-fold increased risk of HCC compared to patients with wild-type for both regions. Conclusions: CP-MT, T1653, HBV DNA levels ≥4 log 10 copies/ml and cirrhosis are independent factors for development of HCC. The risks increased substantially in patients having these factors in combination.published_or_final_versio

Can Gravitational Waves Prevent Inflation?

To investigate the cosmic no hair conjecture, we analyze numerically 1-dimensional plane symmetrical inhomogeneities due to gravitational waves in vacuum spacetimes with a positive cosmological constant. Assuming periodic gravitational pulse waves initially, we study the time evolution of those waves and the nature of their collisions. As measures of inhomogeneity on each hypersurface, we use the 3-dimensional Riemann invariant ${\cal I}\equiv {}~^{(3)\!}R_{ijkl}~^{(3)\!}R^{ijkl}$ and the electric and magnetic parts of the Weyl tensor. We find a temporal growth of the curvature in the waves' collision region, but the overall expansion of the universe later overcomes this effect. No singularity appears and the result is a ``no hair" de Sitter spacetime. The waves we study have amplitudes between $0.020\Lambda \leq {\cal I}^{1/2} \leq 125.0\Lambda$ and widths between $0.080l_H \leq l \leq 2.5l_H$, where $l_H=(\Lambda/3)^{-1/2}$, the horizon scale of de Sitter spacetime. This supports the cosmic no hair conjecture.Comment: LaTeX, 11 pages, 3 figures are available on request <To [email protected] (Hisa-aki SHINKAI)>, WU-AP/29/9

Gravitational Waves in Brans-Dicke Theory : Analysis by Test Particles around a Kerr Black Hole

Analyzing test particles falling into a Kerr black hole, we study gravitational waves in Brans-Dicke theory of gravity. First we consider a test particle plunging with a constant azimuthal angle into a rotating black hole and calculate the waveform and emitted energy of both scalar and tensor modes of gravitational radiation. We find that the waveform as well as the energy of the scalar gravitational waves weakly depends on the rotation parameter of black hole $a$ and on the azimuthal angle. Secondly, using a model of a non-spherical dust shell of test particles falling into a Kerr black hole, we study when the scalar modes dominate. When a black hole is rotating, the tensor modes do not vanish even for a ``spherically symmetric" shell, instead a slightly oblate shell minimizes their energy but with non-zero finite value, which depends on Kerr parameter $a$. As a result, we find that the scalar modes dominate only for highly spherical collapse, but they never exceed the tensor modes unless the Brans-Dicke parameter \omega_{BD} \lsim 750 for $a/M=0.99$ or unless \omega_{BD} \lsim 20,000 for $a/M=0.5$, where $M$ is mass of black hole. We conclude that the scalar gravitational waves with \omega_{BD} \lsim several thousands do not dominate except for very limited situations (observation from the face-on direction of a test particle falling into a Schwarzschild black hole or highly spherical dust shell collapse into a Kerr black hole). Therefore observation of polarization is also required when we determine the theory of gravity by the observation of gravitational waves.Comment: 24 pages, revtex, 18 figures are attached with ps file