Einstein boundary conditions for the Einstein equations in the conformal-traceless decomposition

In relation to the BSSN formulation of the Einstein equations, we write down the boundary conditions that result from the vanishing of the projection of the Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up a well-posed system of propagation equations for the constraints, we show explicitly that there are three constraints that are incoming at the boundary surface and that the boundary equations are linearly related to them. This indicates that such boundary conditions play a role in enforcing the propagation of the constraints in the region interior to the boundary. Additionally, we examine the related problem for a strongly hyperbolic first-order reduction of the BSSN equations and determine the characteristic fields that are prescribed by the three boundary conditions, as well as those that are left arbitrary.Comment: 11 page

Robustness of the Blandford-Znajek mechanism

The Blandford-Znajek mechanism has long been regarded as a key ingredient in models attempting to explain powerful jets in AGNs, quasars, blazzars etc. In such mechanism, energy is extracted from a rotating black hole and dissipated at a load at far distances. In the current work we examine the behaviour of the BZ mechanism with respect to different boundary conditions, revealing the mechanism robustness upon variation of these conditions. Consequently, this work closes a gap in our understanding of this important scenario.Comment: 7 pages, accepted in CQ

3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints

We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for the associated initial-boundary value problem. The code is first tested with a gauge wave solution, where rather larger amplitudes and for significantly longer times are obtained with respect to other state of the art implementations. Additionally, by minimizing a suitably defined energy for the constraints in terms of free constraint-functions in the formulation one can dynamically single out preferred values of these functions for the problem at hand. We apply the technique to fully three-dimensional simulations of a stationary black hole spacetime with excision of the singularity, considerably extending the lifetime of the simulations.Comment: 21 pages. To appear in PR

Simulating binary neutron stars: dynamics and gravitational waves

We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow us to compute the orbital kinematics, including trajectories and orbital eccentricities. We verify our code by evolving single stars and extracting radial perturbative modes, which compare very well to results from perturbation theory. The Einstein equations are solved in a first order reduction of the generalized harmonic formulation, and the fluid equations are solved using a modified convex essentially non-oscillatory method. All calculations are done in three spatial dimensions without symmetry assumptions. We use the \had computational infrastructure for distributed adaptive mesh refinement.Comment: 14 pages, 16 figures. Added one figure from previous version; corrected typo

Boundary conditions for hyperbolic formulations of the Einstein equations

In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of equivalent formulations. We explicitly show that this is so for the Einstein-Christoffel formulation of the Einstein equations in the case of spherical symmetry.Comment: 15 pages; text added and typesetting errors corrected; to appear in Classical and Quantum Gravit

Deep ACS Imaging in the Globular Cluster NGC 6397: The Cluster Color Magnitude Diagram and Luminosity Function

We present the CMD from deep HST imaging in the globular cluster NGC 6397. The ACS was used for 126 orbits to image a single field in two colors (F814W, F606W) 5 arcmin SE of the cluster center. The field observed overlaps that of archival WFPC2 data from 1994 and 1997 which were used to proper motion (PM) clean the data. Applying the PM corrections produces a remarkably clean CMD which reveals a number of features never seen before in a globular cluster CMD. In our field, the main sequence stars appeared to terminate close to the location in the CMD of the hydrogen-burning limit predicted by two independent sets of stellar evolution models. The faintest observed main sequence stars are about a magnitude fainter than the least luminous metal-poor field halo stars known, suggesting that the lowest luminosity halo stars still await discovery. At the bright end the data extend beyond the main sequence turnoff to well up the giant branch. A populous white dwarf cooling sequence is also seen in the cluster CMD. The most dramatic features of the cooling sequence are its turn to the blue at faint magnitudes as well as an apparent truncation near F814W = 28. The cluster luminosity and mass functions were derived, stretching from the turn off down to the hydrogen-burning limit. It was well modeled with either a very flat power-law or a lognormal function. In order to interpret these fits more fully we compared them with similar functions in the cluster core and with a full N-body model of NGC 6397 finding satisfactory agreement between the model predictions and the data. This exercise demonstrates the important role and the effect that dynamics has played in altering the cluster IMF.Comment: 43 pages including 4 tables and 12 diagrams. Figures 2 and 3 have been bitmapped. Accepted for publication in the Astronomical Journa

Thermal phenomenology of hadrons from 200 AGeV S+S collisions

We develop a complete and consistent description for the hadron spectra from heavy ion collisions in terms of a few collective variables, in particular temperature, longitudinal and transverse flow. To achieve a meaningful comparison with presently available data, we also include the resonance decays into our picture. To disentangle the influences of transverse flow and resonance decays in the $m_T$-spectra, we analyse in detail the shape of the $m_T$-spectra.Comment: 31 pages, 13 figs in seperate uuencoded file, for LaTeX, epsf.sty and dvips, TPR-93-16 and BNL-(no number yet

High-powered Gravitational News

We describe the computation of the Bondi news for gravitational radiation. We have implemented a computer code for this problem. We discuss the theory behind it as well as the results of validation tests. Our approach uses the compactified null cone formalism, with the computational domain extending to future null infinity and with a worldtube as inner boundary. We calculate the appropriate full Einstein equations in computational eth form in (a) the interior of the computational domain and (b) on the inner boundary. At future null infinity, we transform the computed data into standard Bondi coordinates and so are able to express the news in terms of its standard $N_{+}$ and $N_{\times}$ polarization components. The resulting code is stable and second-order convergent. It runs successfully even in the highly nonlinear case, and has been tested with the news as high as 400, which represents a gravitational radiation power of about $10^{13}M_{\odot}/sec$.Comment: 24 pages, 4 figures. To appear in Phys. Rev.

Improved Laboratory Transition Probabilities for Neutral Chromium and Re-determination of the Chromium Abundance for the Sun and Three Stars

Branching fraction measurements from Fourier transform spectra in conjunction with published radiative lifetimes are used to determine transition probabilities for 263 lines of neutral chromium. These laboratory values are employed to derive a new photospheric abundance for the Sun: log $\epsilon$(Cr I)$_{\odot}$ = 5.64$\pm$0.01 ($\sigma = 0.07$). These Cr I solar abundances do not exhibit any trends with line strength nor with excitation energy and there were no obvious indications of departures from LTE. In addition, oscillator strengths for singly-ionized chromium recently reported by the FERRUM Project are used to determine: log $\epsilon$(Cr II)$_{\odot}$ = 5.77$\pm$0.03 ($\sigma = 0.13$). Transition probability data are also applied to the spectra of three stars: HD 75732 (metal-rich dwarf), HD 140283 (metal-poor subgiant), and CS 22892-052 (metal-poor giant). In all of the selected stars, Cr I is found to be underabundant with respect to Cr II. The possible causes for this abundance discrepancy and apparent ionization imbalance are discussed.Comment: 44 pages, 6 figure

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls