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

Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole

Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary conditions where the lapse arises as a linear combination of odd and even lapse. Favorable boundary conditions are then derived which make the overall slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding in addition that a numerically favorable lapse remains non-negative, as result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally, analytic arguments are given on how slice stretching effects can be avoided. Here the excision technique and the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice stretching can be avoided by using excision and/or shift

UV Interstellar Absorption Lines towards the Starburst Dwarf Galaxy NGC 1705

Archival Goddard High Resolution Spectrograph low-resolution spectra of NGC 1705, with wavelength ranges 1170.3 to 1461.7 A and 1453.5 to 1740.1 A and a velocity resolution of about 100 km\s, have been used to derive the velocity structure and equivalent widths of the absorption lines of Si II 1190.42, 1260.42, 1304.37 and 1526.71 A, S II 1253 , Al II 1670.79 Aand Fe II 1608.45 A in this sightline. Three relatively narrow absorption components are seen at LSR velocities --20 km/s, 260 km/sand 540 km/s. Arguments are presented to show these absorption features are interstellar rather than stellar in origin based on a comparison with the C III 1175.7 A absorption feature. We identify the --20 km/s component with Milky Way disk/halo gas and the 260 km/s component with an isolated high-velocity cloud HVC 487. This small HVC is located about 10 degrees from the H I gas which envelops the Magellanic Clouds and the Magellanic Stream (MS). The (Si/H) ratio for this HVC is > 0.6 (Si/H)solar which together with velocity agreement, suggests association with the Magellanic Cloud and MS gas. H-alpha emission line kinematics of NGC 1705 show the presence of a kpc-scale expanding supershell of ionized gas centered on the central nucleus with a blue-shifted emission component at 540 km/s (Meurer et al. 1992). We identify the 540 km/s absorption component seen in the GHRS spectra with the front side of this expanding, ionized supershell. The most striking feature of this component is strong Si II and Al II absorption but weak Fe II 1608 A absorption. The low Fe II column density derived is most likely intrinsic since it cannot be accounted for by ionization corrections or dust depletion. Due to their shallow gravitational potential wells, dwarf galaxies have small gravitational binding energies and are vulnerable to largeComment: 15 pages, LaTEX, 1 figure. Accepted for publication in Astrophysical Journal Letter

Local and global properties of conformally flat initial data for black hole collisions

We study physical properties of conformal initial value data for single and binary black hole configurations obtained using conformal-imaging and conformal-puncture methods. We investigate how the total mass M_tot of a dataset with two black holes depends on the configuration of linear or angular momentum and separation of the holes. The asymptotic behavior of M_tot with increasing separation allows us to make conclusions about an unphysical ``junk'' gravitation field introduced in the solutions by the conformal approaches. We also calculate the spatial distribution of scalar invariants of the Riemann tensor which determine the gravitational tidal forces. For single black hole configurations, these are compared to known analytical solutions. Spatial distribution of the invariants allows us to make certain conclusions about the local distribution of the additional field in the numerical datasets

High-Redshift Superclustering of QSO Absorption Line Systems on 100 Mpc Scales

We have analyzed the clustering of C IV absorption line systems in an extensive new catalog of heavy element QSO absorbers. The catalog permits exploration of clustering over a large range in both scale (from about 1 to over 300 Mpc) and redshift (z from 1.2 to 4.5). We find significant evidence (5.0 sigma) that C IV absorbers are clustered on comoving scales of 100 Mpc and less --- similar to the size of voids and walls found in galaxy redshift surveys of the local universe --- with a mean correlation function $\xi = 0.42 \pm 0.10$ over these scales. We find, on these scales, that the mean correlation function at low (z=1.7), medium (z=2.4), and high redshift (z=3.0) is $\xi=0.40 \pm 0.17$, $0.32 \pm 0.14$, and $0.72 \pm 0.25$, respectively. Thus, the superclustering is present even at high redshift; furthermore, it does not appear that the superclustering scale, in comoving coordinates, has changed significantly since then. We find 7 QSOs with rich groups of absorbers (potential superclusters) that account for a significant portion of the clustering signal, with 2 at redshift $z\sim 2.8$. We find that the superclustering is just as evident if we take $q_0=0.1$ instead of 0.5; however, the inferred scale of clustering is then 240 Mpc , which is larger than the largest scales of clustering known at present. This discrepancy may be indicative of a larger value of $q_0$, and hence $\Omega_0$. The evolution of the correlation function on 50 Mpc scales is consistent with that expected in cosmologies with density parameter ranging from $\Omega_0 =$ 0.1 to 1. Finally, we find no evidence for clustering on scales greater than 100 Mpc ($q_0=0.5$) or 240 Mpc ($q_0=0.1$).Comment: 16 LaTeX pages with 3 encapsulated Postscript figures included, uses AASTeX (v. 4.0) available at ftp://ftp.aas.org/pubs/ , to appear in The Astrophysical Journal Letter

Scale-invariant gravity: Spacetime recovered

The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Recently a manifestly 3-dimensional theory was constructed with conformal superspace as the configuration space. Here a fully 4-dimensional action is constructed so as to be invariant under conformal transformations of the 4-metric using general relativity as a guide. This action is then decomposed to a (3+1)-dimensional form and from this to its Jacobi form. The surprising thing is that the new theory turns out to be precisely the original 3-dimensional theory. The physical data is identified and used to find the physical representation of the theory. In this representation the theory is extremely similar to general relativity. The clarity of the 4-dimensional picture should prove very useful for comparing the theory with those aspects of general relativity which are usually treated in the 4-dimensional framework.Comment: Replaced with final version: minor changes to tex

Excision boundary conditions for black hole initial data

We define and extensively test a set of boundary conditions that can be applied at black hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasi-circular orbits and the determination of the inner-most stable circular orbit. Our tests show that the boundary conditions work well.Comment: 23 pages, 23 figures, revtex4, corrected typos, added reference, minor content changes including additional post-Newtonian comparison. Version accepted by PR

Wall jet analysis for circulation control aerodynamics. Part 1: Fundamental CFD and turbulence modeling concepts

An overview of parabolic and PNS (Parabolized Navier-Stokes) methodology developed to treat highly curved sub and supersonic wall jets is presented. The fundamental data base to which these models were applied is discussed in detail. The analysis of strong curvature effects was found to require a semi-elliptic extension of the parabolic modeling to account for turbulent contributions to the normal pressure variations, as well as an extension to the turbulence models utilized, to account for the highly enhanced mixing rates observed in situations with large convex curvature. A noniterative, pressure split procedure is shown to extend parabolic models to account for such normal pressure variations in an efficient manner, requiring minimal additional run time over a standard parabolic approach. A new PNS methodology is presented to solve this problem which extends parabolic methodology via the addition of a characteristic base wave solver. Applications of this approach to analyze the interaction of wave and turbulence processes in wall jets is presented

The warp drive: hyper-fast travel within general relativity

It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the ``warp drive'' of science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion of spacetime like the one discussed here.Comment: 10 pages, 1 figure. Not previously available in gr-q