Moral Philosophy and the Analysis of Language

This is the text of The Lindley Lecture for 1963, given by Richard B. Brandt (1910-1997), an American philosopher

Solving the Initial Value Problem of two Black Holes

We solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild spacetime slicing which provides more physically realistic solutions than the initial data based on conformally flat metric/maximal slicing methods. The singularity/inner boundary problems are circumvented by a new technique that allows the use of an elliptic solver on a Cartesian grid where no points are excised, simplifying enormously the numerical problem.Comment: 4 pages, 3 figures. Minor corrections, some points clarified, and one reference added. To appear in Phys. Rev. Let

Approximate Analytical Solutions to the Initial Data Problem of Black Hole Binary Systems

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these initial data solutions makes them easier to implement in numerical evolutions than the traditional numerical approach of solving the elliptic equations derived from the Einstein constraints. Although in general the problem of setting up initial conditions for black hole binary simulations is complicated by the presence of singularities, we show that the methods presented in this work provide initial data with $l_1$ and $l_\infty$ norms of violation of the constraint equations falling below those of the truncation error (residual error due to discretization) present in finite difference codes for the range of grid resolutions currently used. Thus, these data sets are suitable for use in evolution codes. Detailed results are presented for the case of a head-on collision of two equal-mass M black holes with specific angular momentum 0.5M at an initial separation of 10M. A straightforward superposition method yields data adequate for resolutions of $h=M/4$, and an "attenuated" superposition yields data usable to resolutions at least as fine as $h=M/8$. In addition, the attenuated approximate data may be more tractable in a full (computational) exact solution to the initial value problem.Comment: 6 pages, 5 postscript figures. Minor changes and some points clarified. Accepted for publication in Phys. Rev.

Evolving the Bowen-York initial data for spinning black holes

The Bowen-York initial value data typically used in numerical relativity to represent spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes.Comment: 10 pages, RevTeX, 4 figures included with psfi

The collision of boosted black holes: second order close limit calculations

We study the head-on collision of black holes starting from unsymmetrized, Brill--Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the ``close limit approximation,'' in which small initial separation and momentum are assumed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calculations were used for momentarily stationary initial data, and another study in which linearized perturbation theory was used for initially moving holes. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbation theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulations, and will be important to subsequent applications of approximation methods for collisions.Comment: 20 pages, RevTeX, 6 figures included with psfi

The collision of boosted black holes

We study the radiation from a collision of black holes with equal and opposite linear momenta. Results are presented from a full numerical relativity treatment and are compared with the results from a ``close-slow'' approximation. The agreement is remarkable, and suggests several insights about the generation of gravitational radiation in black hole collisions.Comment: 8 pages, RevTeX, 3 figures included with eps

NASA's Single-Pilot Operations Technical Interchange Meeting: Proceedings and Findings

Researchers at the National Aeronautics and Space Administration (NASA) Ames Research Center and Langley Research Center are jointly investigating issues associated with potential concepts, or configurations, in which a single pilot might operate under conditions that are currently reserved for a minimum of two pilots. As part of early efforts, NASA Ames Research Center hosted a technical interchange meeting in order to gain insight from members of the aviation community regarding single-pilot operations (SPO). The meeting was held on April 10-12, 2012 at NASA Ames Research Center. Professionals in the aviation domain were invited because their areas of expertise were deemed to be directly related to an exploration of SPO. NASA, in selecting prospective participants, attempted to represent various relevant sectors within the aviation domain. Approximately 70 people representing government, academia, and industry attended. A primary focus of this gathering was to consider how tasks and responsibilities might be re-allocated to allow for SPO

Initial Data and Coordinates for Multiple Black Hole Systems

We present here an alternative approach to data setting for spacetimes with multiple moving black holes generalizing the Kerr-Schild form for rotating or non-rotating single black holes to multiple moving holes. Because this scheme preserves the Kerr-Schild form near the holes, it selects out the behaviour of null rays near the holes, may simplify horizon tracking, and may prove useful in computational applications. For computational evolution, a discussion of coordinates (lapse function and shift vector) is given which preserves some of the properties of the single-hole Kerr-Schild form

The Ionized Gas and Nuclear Environment in NGC 3783. I. Time-Averaged 900 ks Chandra Grating Spectroscopy

We present results from a 900 ks exposure of NGC 3783 with the High-Energy Transmission Grating Spectrometer on board the Chandra X-ray Observatory. The resulting X-ray spectrum has the best combination of signal-to-noise and resolution ever obtained for an AGN. This spectrum reveals absorption lines from H-like and He-like ions of N, O, Ne, Mg, Al, Si, and S. There are also possible absorption lines from H-like and He-like Ar and Ca. We also identify inner-shell absorption from lower-ionization ions such as Si_VII-Si_XII and S_XII-S_XIV. The iron absorption spectrum is very rich; L-shell lines of Fe_XVII-Fe_XXIV are detected, strong complex of M-shell lines, and probable resonance lines from Fe_XXV. The absorption lines are blueshifted relative to the systemic velocity by a mean velocity of -590+-150 km/s. We resolve many of the absorption lines, and their mean FWHM is 820+-280 km/s. We do not find correlations between the velocity shifts or the FWHMs with the ionization potentials of the ions. Most absorption lines show asymmetry, having more extended blue wings than red wings. In O_VII we have resolved this asymmetry to be from an additional absorption system at ~ -1300 km/s. The two X-ray absorption systems are consistent in velocity shift and FWHM with the ones identified in the UV lines of C IV, N V, and H I. Equivalent width measurements for all lines are given and column densities are calculated for several ions. We resolve the narrow Fe_K\alpha line at 6398.2+-3.3 eV to have a FWHM of 1720+-360 km/s, which suggests that this narrow line may be emitted from the outer part of the broad line region or the inner part of the torus. We also detect a `Compton shoulder' redward of the narrow Fe_K\alpha line which indicates that it arises in cold, Compton-thick gas.Comment: 19 pages, 12 figures (2 in color), emulateapj5, accepted for publication in The Astrophysical Journal Supplement