Ellipsoidal shapes in general relativity: general definitions and an application

A generalization of the notion of ellipsoids to curved Riemannian spaces is given and the possibility to use it in describing the shapes of rotating bodies in general relativity is examined. As an illustrative example, stationary, axisymmetric perfect-fluid spacetimes with a so-called confocal inside ellipsoidal symmetry are investigated in detail under the assumption that the 4-velocity of the fluid is parallel to a time-like Killing vector field. A class of perfect-fluid metrics representing interior NUT-spacetimes is obtained along with a vacuum solution with a non-zero cosmological constant.Comment: Latex, 22 pages, Revised version accepted in Class. Quantum. Grav., references adde

Black holes and a scalar field in an expanding universe

We consider a model of an inhomogeneous universe including a massless scalar field, where the inhomogeneity is assumed to consist of many black holes. This model can be constructed by following Lindquist and Wheeler, which has already been investigated without including scalar field to show that an averaged scale factor coincides with that of the Friedmann model. In this work we construct the inhomogeneous universe with an massless scalar field, where we assume that the averaged scale factor and scalar field are given by those of the Friedmann model including a scalar field. All of our calculations are carried out in the framework of Brans-Dicke gravity. In constructing the model of an inhomogeneous universe, we define the mass of a black hole in the Brans-Dicke expanding universe which is equivalent to ADM mass if the mass evolves adiabatically, and obtain an equation relating our mass to the averaged scalar field and scale factor. As the results we find that the mass has an adiabatic time dependence in a sufficiently late stage of the expansion of the universe, and that the time dependence is qualitatively diffenrent according to the sign of the curvature of the universe: the mass increases decelerating in the closed universe case, is constant in the flat case and decreases decelerating in the open case. It is also noted that the mass in the Einstein frame depends on time. Our results that the mass has a time dependence should be retained even in the general scalar-tensor gravitiy with a scalar field potential. Furthermore, we discuss the relation of our results to the uniqueness theorem of black hole spacetime and gravitational memory effect.Comment: 16 pages, 3 tables, 5 figure

X-Ray Observations of the supernova remnant G21.5-0.9

We present the analysis of archival X-ray observations of the supernova remnant (SNR) G21.5-0.9. Based on its morphology and spectral properties, G21.5-0.9 has been classified as a Crab-like SNR. In their early analysis of the CHANDRA calibration data, Slane et al. (2000) discovered a low-surface-brightness, extended emission. They interpreted this component as the blast wave formed in the supernova (SN) explosion. In this paper, we present the CHANDRA analysis using a total exposure of ~150 ksec. We also include ROSAT and ASCA observations. Our analysis indicates that the extended emission is non-thermal -- a result in agreement with XMM observations. The entire remnant of radius ~ 2'.5 is best fitted with a power law model with a photon index steepening away from the center. The total unabsorbed flux in the 0.5-10 keV is 1.1E-10 erg/cm2/s with an 85% contribution from the 40" radius inner core. Timing analysis of the High-Resolution Camera (HRC) data failed to detect any pulsations. We put a 16% upper limit on the pulsed fraction. We derive the physical parameters of the putative pulsar and compare them with those of other plerions (such as the Crab and 3C 58). G21.5-0.9 remains the only plerion whose size in X-rays is bigger than in the radio. Deep radio observations will address this puzzle.Comment: 23 pages including 11 figures and 3 tables; accepted by ApJ June 22, 2001; to appear in Oct 20, 2001 issue of Ap

Lensing and caustic effects on cosmological distances

We consider the changes which occur in cosmological distances due to the combined effects of some null geodesics passing through low-density regions while others pass through lensing-induced caustics. This combination of effects increases observed areas corresponding to a given solid angle even when averaged over large angular scales, through the additive effect of increases on all scales, but particularly on micro-angular scales; however angular sizes will not be significantly effected on large angular scales (when caustics occur, area distances and angular-diameter distances no longer coincide). We compare our results with other works on lensing, which claim there is no such effect, and explain why the effect will indeed occur in the (realistic) situation where caustics due to lensing are significant. Whether or not the effect is significant for number counts depends on the associated angular scales and on the distribution of inhomogeneities in the universe. It could also possibly affect the spectrum of CBR anisotropies on small angular scales, indeed caustics can induce a non-Gaussian signature into the CMB at small scales and lead to stronger mixing of anisotropies than occurs in weak lensing.Comment: 28 pages, 6 ps figures, eps

A linear programming-based method for job shop scheduling

We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach

On the stability of fissured slopes subject to seismic action

A set of analytical solutions achieved by the upper bound theorem of limit analysis and the pseudo-static approach is presented for the assessment of the stability of homogeneous c, ϕ slopes manifesting vertical cracks and subject to seismic action. Rotational failure mechanisms are considered for slopes with cracks of either known or unknown depth and location. A validation exercise was carried out based on numerical limit analyses and displacement-based finite-element analyses with strength reduction technique. Charts providing the stability factor for fissured slopes subject to both horizontal and vertical accelerations for any combination of c, ϕ and slope inclination are provided. The effect of the direction of the vertical acceleration on slope stability is specifically analysed. Yield seismic coefficients are also provided. When the presence of cracks within the slope can be ascertained with reasonable confidence, maps showing the zones within the slope where they have no destabilising effect are provided. Finally, Newmark's method was employed to assess the effect of cracks on earthquake induced displacements. To this end, displacement coefficients are provided in chart form as a function of the slope characteristics. Two examples of slopes subjected to known earthquakes are illustrated

Reanalysis of the Apollo cosmic gamma-ray spectrum in the 0.3 to 10 MeV energy region

Additional data obtained from the Apollo-16 and -17 missions, together with collateral calculations on background radiation effects, have enabled an improved subtraction of unwanted backgrounds from the diffuse cosmic gamma-ray data previously reported from Apollo-15. As a result, the 1- to 10-MeV spectrum is lowered significantly and connects smoothly with recent data at other energies. The inflection reported previously is much less pronounced and has no more than a 1.5-sigma significance. Sky occultation by the Apollo-16 spacecraft shows the bulk of the 0.3- to 1-MeV radiation to be diffuse. The analysis of spurious backgrounds points to important improvements for future experiments designed for this spectral region

Diffuse Hard X-ray Sources Discovered with the ASCA Galactic Plane Survey

We found diffuse hard X-ray sources, G11.0+0.0, G25.5+0.0, and G26.6-0.1 in the ASCA Galactic plane survey data. The X-ray spectra are featureless with no emission line, and are fitted with both models of a thin thermal plasma in non-equilibrium ionization and a power-law function. The source distances are estimated to be 1-8 kpc, using the best-fit NH values on the assumption that the mean density in the line of sight is 1 H cm^-3. The source sizes and luminosities are then 4.5-27 pc and (0.8-23)x10^33 ergs/s. Although the source sizes are typical to supernova remnants (SNR) with young to intermediate ages, the X-ray luminosity, plasma temperature, and weak emission lines in the spectra are all unusual. This suggests that these objects are either shell-like SNRs dominated by X-ray synchrotron emission, like SN 1006, or, alternatively, plerionic SNRs. The total number of these classes of SNRs in our Galaxy is also estimated.Comment: 17 pages, 9 figures; to appear in Ap