Topics in the Dynamics or General Relativity

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Maximal Hypersurfaces and Positivity of Mass

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Method for reducing snap in magnetic amplifiers

Method of reducing snap in magnetic amplifiers uses a degenerative feedback circuit consisting of a resistor and a separate winding on a magnetic core. The feedback circuit extends amplifier range by allowing it to be used at lower values of output current

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

Speed Limits in General Relativity

Some standard results on the initial value problem of general relativity in matter are reviewed. These results are applied first to show that in a well defined sense, finite perturbations in the gravitational field travel no faster than light, and second to show that it is impossible to construct a warp drive as considered by Alcubierre (1994) in the absence of exotic matter.Comment: 7 pages; AMS-LaTeX; accepted for publication by Classical and Quantum Gravit

Thermal Conductivity of Single Wall Carbon Nanotubes: Diameter and Annealing Dependence

The thermal conductivity, k(T), of bulk single-wall carbon nanotubes (SWNT's) displays a linear temperature dependence at low T that has been attributed to 1D quantization of phonons. To explore this issue further, we have measured the k(T) of samples with varying average tube diameters. We observe linear k(T) up to higher temperatures in samples with smaller diameters, in agreement with a quantization picture. In addition, we have examined the effect of annealing on k(T). We observe an enhancement in k(T) for annealed samples which we attribute to healing of defects and removal of impurities. These measurements demonstrate how the thermal properties of an SWNT material can be controlled by manipulating its intrinsic nanoscale properties.Comment: Proc. of the XV. Int. Winterschool on Electronic Properties of Novel Materials, Kirchberg/Tirol, Austria, 200

Inflowing gas onto a compact obscured nucleus in Arp 299A: Herschel spectroscopic studies of H2O and OH

Aims. We probe the physical conditions in the core of Arp 299A and try to put constraints to the nature of its nuclear power source. Methods. We used Herschel Space Observatory far-infrared and submillimeter observations of H2O and OH rotational lines in Arp 299A to create a multi-component model of the galaxy. In doing this, we employed a spherically symmetric radiative transfer code. Results. Nine H2O lines in absorption and eight in emission as well as four OH doublets in absorption and one in emission, are detected in Arp 299A. No lines of the 18O isotopologues, which have been seen in compact obscured nuclei of other galaxies, are detected. The absorption in the ground state OH doublet at 119 {\mu}m is found redshifted by ~175 km/s compared to other OH and H2O lines, suggesting a low excitation inflow. We find that at least two components are required in order to account for the excited molecular line spectrum. The inner component has a radius of 20-25 pc, a very high infrared surface brightness (> 3e13 Lsun/kpc^2), warm dust (Td > 90 K), and a large H2 column density (NH2 > 1e24 cm^-2). The outer component is larger (50-100 pc) with slightly cooler dust (70-90 K). In addition, a much more extended inflowing component is required to also account for the OH doublet at 119 {\mu}m. Conclusions. The Compton-thick nature of the core makes it difficult to determine the nature of the buried power source, but the high surface brightness indicates that it is either an active galactic nucleus and/or a dense nuclear starburst. The high OH/H2O ratio in the nucleus indicates that ion-neutral chemistry induced by X-rays or cosmic-rays is important. Finally we find a lower limit to the 16O/18O ratio of 400 in the nuclear region, possibly indicating that the nuclear starburst is in an early evolutionary stage, or that it is fed through a molecular inflow of, at most, solar metallicity.Comment: 14 pages, 13 figures, Accepted for publication in Astronomy and Astrophysic

Modeling the H2O submillimeter emission in extragalactic sources

Recent observational studies have shown that H2O emission at (rest) submillimeter wavelengths is ubiquitous in infrared galaxies, both in the local and in the early Universe, suggestive of far-infrared pumping of H2O by dust in warm regions. In this work, models are presented that show that (i) the highest-lying H2O lines (E_{upper}>400 K) are formed in very warm (T_{dust}>~90 K) regions and require high H2O columns (N_{H2O}>~3x10^{17} cm^{-2}), while lower lying lines can be efficiently excited with T_{dust}~45-75 K and N_{H2O}~(0.5-2)x10^{17} cm^{-2}; (ii) significant collisional excitation of the lowest lying (E_{upper}<200 K) levels, which enhances the overall L_{H2O}-L_{IR} ratios, is identified in sources where the ground-state para-H2O 1_{11}-0_{00} line is detected in emission; (iii) the H2O-to-infrared (8-1000 um) luminosity ratio is expected to decrease with increasing T_{dust} for all lines with E_{upper}<~300 K, as has recently been reported in a sample of LIRGs, but increases with T_{dust} for the highest lying H2O lines (E_{upper}>400 K); (iv) we find theoretical upper limits for L_{H2O}/L_{IR} in warm environments, owing to H2O line saturation; (v) individual models are presented for two very different prototypical galaxies, the Seyfert 2 galaxy NGC 1068 and the nearest ultraluminous infrared galaxy Arp 220, showing that the excited submillimeter H2O emission is dominated by far-infrared pumping in both cases; (vi) the L_{H2O}-L_{IR} correlation previously reported in observational studies indicates depletion or exhaustion time scales, t_{dep}=Sigma_{gas}/Sigma_{SFR}, of <~12 Myr for star-forming sources where lines up to E_{upper}=300 K are detected, in agreement with the values previously found for (U)LIRGs from HCN millimeter emission...Comment: 13 pages, 13 figure

Emissivity measurements of reflective surfaces at near-millimeter wavelengths

We have developed an instrument for directly measuring the emissivity of reflective surfaces at near-millimeter wavelengths. The thermal emission of a test sample is compared with that of a reference surface, allowing the emissivity of the sample to be determined without heating. The emissivity of the reference surface is determined by one’s heating the reference surface and measuring the increase in emission. The instrument has an absolute accuracy of Δe = 5 x 10^-4 and can reproducibly measure a difference in emissivity as small as Δe = 10^-4 between flat reflective samples. We have used the instrument to measure the emissivity of metal films evaporated on glass and carbon fiber-reinforced plastic composite surfaces. We measure an emissivity of (2.15 ± 0.4) x 10^-3 for gold evaporated on glass and (2.65 ± 0.5) x 10^-3 for aluminum evaporated on carbon fiber-reinforced plastic composite

The nonrelativistic limit of Dirac-Fock codes: the role of Brillouin configurations

We solve a long standing problem with relativistic calculations done with the widely used Multi-Configuration Dirac-Fock Method (MCDF). We show, using Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively high-$Z$, relaxation or correlation causes the non-relativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We show that only large scale calculations that include all single excitations, even those obeying the Brillouin's theorem have the correct limit. We reproduce very accurately recent high-precision measurements in F-like Ar, and turn then into precise test of QED. We obtain the correct non-relativistic limit not only for fine structure but also for level energies and show that RMBPT calculations are not immune to this problem.Comment: AUgust 9th, 2004 Second version Nov. 18th, 200