Hyperbolicity and Constrained Evolution in Linearized Gravity

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them ({\it unconstrained} evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly "more correct" to introduce a scheme which actively maintains the constraints by solution ({\it constrained} evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations.Comment: 18 page

The Stanley Foundation Bipolar Network: Results of the naturalistic follow-up study after 2.5 years of follow-up in the German centres

The Stanley Foundation Bipolar Network (SFBN) is an international, multisite network investigating the characteristics and course of bipolar disorder. Methods (history, ratings and longitudinal follow-up) are standardized and equally applied in all 7 centres. This article describes demographics and illness characteristics of the first 152 German patients enrolled in them SFBN as well as the results of 2.5 years of follow-up. Patients in Germany were usually enrolled after hospitalisation. More than 72% of the study population suffered from bipolar I disorder and 25% from bipolar 11 disorder. The mean +/- SD age of the study participants was 42.08 +/- 13.5 years, and the mean SD age of onset 24.44 +/- 10.9 years. More than 40% of the sample reported a rapid-cycling course in history, and even more a cycle acceleration overtime. 37% attempted suicide at least once. 36% had an additional Axis I disorder, with alcohol abuse being the most common one, followed by anxiety disorders. During the follow-up period, only 27% remained stable, 56% had a recurrence, 12.8% perceived subsyndromal symptoms despite treatment and regular visits. 27% suffered from a rapid-cycling course during the follow-up period. Recurrences were significantly associated with bipolar I disorder, an additional comorbid Axis I disorder, rapid cycling in history, a higher number of mood stabilizers and the long-term use of typical antipsychotics. Rapid cycling during follow-up was only associated with a rapidcycling course in history, a higher number of mood stabilizers and at least one suicide attempt in history. Copyright (c) 2003 S. Karger AG, Basel

Close limit evolution of Kerr-Schild type initial data for binary black holes

We evolve the binary black hole initial data family proposed by Bishop {\em et al.} in the limit in which the black holes are close to each other. We present an exact solution of the linearized initial value problem based on their proposal and make use of a recently introduced generalized formalism for studying perturbations of Schwarzschild black holes in arbitrary coordinates to perform the evolution. We clarify the meaning of the free parameters of the initial data family through the results for the radiated energy and waveforms from the black hole collision.Comment: 8 pages, RevTex, four eps figure

The Outer Shock of the Oxygen-Rich Supernova Remnant G292.0+1.8: Evidence for the Interaction with the Stellar Winds from its Massive Progenitor

We study the outer-shock structure of the oxygen-rich supernova remnant G292.0+1.8, using a deep observation with the Chandra X-ray Observatory. We measure radial variations of the electron temperature and emission measure that we identify as the outer shock propagating into a medium with a radially decreasing density profile. The inferred ambient density structure is consistent with models for the circumstellar wind of a massive progenitor star rather than for a uniform interstellar medium. The estimated wind density n_H = 0.1 ~ 0.3 cm^-3) at the current outer radius (~7.7 pc) of the remnant is consistent with a slow wind from a red supergiant (RSG) star. The total mass of the wind is estimated to be ~ 15 - 40 solar mass (depending on the estimated density range), assuming that the wind extended down to near the surface of the progenitor. The overall kinematics of G292.0+1.8 are consistent with the remnant expanding through the RSG wind.Comment: 9 pages (2-column), 5 figures, accepted for Ap

The discrete energy method in numerical relativity: Towards long-term stability

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test problems commonly used in numerical relativity and observe that while we obtain convergent schemes, fast growing modes, or ``artificial instabilities,'' contaminate the solution. We find that these growing modes can partially arise from the lack of a Leibnitz rule for discrete derivatives and discuss ways to limit this spurious growth.Comment: 18 pages, 22 figure

The Green Bank Ammonia Survey: Unveiling the Dynamics of the Barnard 59 star-forming Clump

Understanding the early stages of star formation is a research field of ongoing development, both theoretically and observationally. In this context, molecular data have been continuously providing observational constraints on the gas dynamics at different excitation conditions and depths in the sources. We have investigated the Barnard 59 core, the only active site of star formation in the Pipe Nebula, to achieve a comprehensive view of the kinematic properties of the source. These information were derived by simultaneously fitting ammonia inversion transition lines (1,1) and (2,2). Our analysis unveils the imprint of protostellar feedback, such as increasing line widths, temperature and turbulent motions in our molecular data. Combined with complementary observations of dust thermal emission, we estimate that the core is gravitationally bound following a virial analysis. If the core is not contracting, another source of internal pressure, most likely the magnetic field, is supporting it against gravitational collapse and limits its star formation efficiency.Comment: 18 pages, 18 figure

Gravitational Wave Bursts from Cosmic Superstring Reconnections

We compute the gravitational waveform produced by cosmic superstring reconnections. This is done by first constructing the superstring reconnection trajectory, which closely resembles that of classical, instantaneous reconnection but with the singularities smoothed out due to the string path integral. We then evaluate the graviton vertex operator in this background to obtain the burst amplitude. The result is compared to the detection threshold for current and future gravitational wave detectors, finding that neither bursts nor the stochastic background would be detectable by Advanced LIGO. This disappointing but anticipated conclusion holds even for the most optimistic values of the reconnection probability and loop sizes.Comment: 26 pages, 6 figures; v2: references added and typos correcte

BLAST: The Mass Function, Lifetimes, and Properties of Intermediate Mass Cores from a 50 Square Degree Submillimeter Galactic Survey in Vela (l = ~265)

We present first results from an unbiased 50 deg^2 submillimeter Galactic survey at 250, 350, and 500 micron from the 2006 flight of the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). The map has resolution ranging from 36 arcsec to 60 arcsec in the three submillimeter bands spanning the thermal emission peak of cold starless cores. We determine the temperature, luminosity, and mass of more than one thousand compact sources in a range of evolutionary stages and an unbiased statistical characterization of the population. From comparison with C^(18)O data, we find the dust opacity per gas mass, kappa r = 0.16 cm^2 g^(-1) at 250 micron, for cold clumps. We find that 2% of the mass of the molecular gas over this diverse region is in cores colder than 14 K, and that the mass function for these cold cores is consistent with a power law with index alpha = -3.22 +/- 0.14 over the mass range 14 M_sun < M < 80 M_sun. Additionally, we infer a mass-dependent cold core lifetime of t_c(M) = 4E6 (M/20 M_sun)^(-0.9) years - longer than what has been found in previous surveys of either low or high mass cores, and significantly longer than free fall or likely turbulent decay times. This implies some form of non-thermal support for cold cores during this early stage of star formation.Comment: Accepted for publication in the Astrophysical Journal. Maps available at http://blastexperiment.info

The trace left by signature-change-induced compactification

Recently, it has been shown that an infinite succession of classical signature changes (''signature oscillations'') can compactify and stabilize internal dimensions, and simultaneously leads, after a coarse graining type of average procedure, to an effective (''physical'') space-time geometry displaying the usual Lorentzian metric signature. Here, we consider a minimally coupled scalar field on such an oscillating background and study its effective dynamics. It turns out that the resulting field equation in four dimensions contains a coupling to some non-metric structure, the imprint of the ''microscopic'' signature oscillations on the effective properties of matter. In a multidimensional FRW model, this structure is identical to a massive scalar field evolving in its homogeneous mode.Comment: 15 pages, LaTeX, no figure

Collisions of Cosmic F- and D-strings

Recent work suggests that fundamental and Dirichlet strings, and their (p,q) bound states, may be observed as cosmic strings. The evolution of cosmic string networks, and therefore their observational signals, depends on what happens when two strings collide. We study this in string perturbation theory for collisions between all possible pairs of strings; different cases involve sphere, disk, and annulus amplitudes. The result also depends on the details of compactification; the dependence on ratios of scales is only logarithmic, but this is still numerically important. We study a range of models and parameters, and find that in most cases these strings can be distinguished from cosmic strings that arise as gauge theory solitons.Comment: 42 pages, 7 figures; v.2: added references, expanded discussion of reconnection in field theor