Space-time extensions II

The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by $\gamma$ one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime $(M,g_{ab})$. First, it is shown that it is always possible to select a synchronised family of causal geodesics $\Gamma$ and an open neighbourhood $\mathcal{U}$ of a final segment of $\gamma$ in $M$ such that $\mathcal{U}$ is comprised by members of $\Gamma$, and suitable local coordinates can be defined everywhere on $\mathcal{U}$ provided that $\gamma$ does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime, $(M,g_{ab})$, is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order $k-1$ are bounded on $\mathcal{U}$, and also the line integrals of the components of the $k^{th}$-order covariant derivatives are finite along the members of $\Gamma$---where all the components are meant to be registered with respect to a synchronised frame field on $\mathcal{U}$---then there exists a $C^{k-}$ extension $\Phi: (M,g_{ab}) \rightarrow (\widehat{M},\widehat{g}_{ab})$ so that for each $\bar\gamma\in\Gamma$, which is inextendible in $(M,g_{ab})$, the image, $\Phi\circ\bar\gamma$, is extendible in $(\widehat{M},\widehat{g}_{ab})$. Finally, it is also proved that whenever $\gamma$ does terminate on a topological singularity $(M,g_{ab})$ cannot be generic.Comment: 42 pages, no figures, small changes to match the published versio

Space-Times Admitting Isolated Horizons

We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition -- in precise sense -- of the Schwarzschild metric with a certain free data set propagating tangentially to the horizon. This proves Ashtekar's conjecture about the structure of spacetime near the isolated horizon. The same superposition method applied to the Kerr metric gives another class of vacuum solutions admitting isolated horizons. More generally, a vacuum spacetime admitting any null, non expanding, shear free surface is characterized. The results are applied to show that, generically, the non-rotating isolated horizon does not admit a Killing vector field and a spacetime is not spherically symmetric near a symmetric horizon.Comment: 11 pages, no figure

Dynamic scaling of fronts in the quantum XX chain

The dynamics of the transverse magnetization in the zero-temperature XX chain is studied with emphasis on fronts emerging from steplike initial magnetization profiles. The fronts move with fixed velocity and display a staircase like internal structure whose dynamic scaling is explored both analytically and numerically. The front region is found to spread with time sub-diffusively with the height and the width of the staircase steps scaling as t^(-1/3) and t^1/3, respectively. The areas under the steps are independent of time, thus the magnetization relaxes in quantized "steps" of spin-flips.Comment: 4 pages, 3 eps figures, RevTe

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

Scratching resistance of SiC-rich nano-coatings produced by noble gas ion mixing

SiC-rich nano-layers were produced at room temperature by applying ion beam mixing of various C/Si multilayer structures using argon and xenon ions with energy in the range of 40–120 keV and fluences between 0.25 and 3 × 1016 ions/cm2. The mechanical behavior of the layers was characterized by scratch test. The scratching resistance of the ion mixed samples has been measured by standard scratch test applying an atomic-force microscope with a diamond-coated tip (radius < 15 nm) and they were compared to that measured on Si single crystal. The applied load varied in the range of 4–18 μN. The scratching resistance of the samples correlated with the effective areal density of the SiC; with increasing effective areal density the scratch depth decreases. Above sufficiently high effective areal density of SiC the scratch resistance (hardness) of the produced layer was somewhat higher than that of single crystal silicon. Previously it has been shown that such layers have excellent corrosion resistive properties as well. These findings allow to tune and design the mechanical and chemical properties of the SiC protective coatings

A Note on Hartle-Hawking Vacua

The purpose of this note is to establish the basic properties--- regularity at the horizon, time independence, and thermality--- of the generalized Hartle-Hawking vacua defined in static spacetimes with bifurcate Killing horizon admitting a regular Euclidean section. These states, for free or interacting fields, are defined by a path integral on half the Euclidean section. The emphasis is on generality and the arguments are simple but formal.Comment: 5 pages, LaTe

Casimir effect in the nonequilibrium steady-state of a quantum spin chain

We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely an energy flux driven quantum XX chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux carrying steady state.Comment: 11 page

The efficiency of nitrogen stabilizer at different soil temperatures on the physiological development and productivity of maize (Zea mays L.)

Received: January 29th, 2021 ; Accepted: October 8th, 2021 ; Published: October 20th, 2021 ; Correspondence: [email protected] (N) stabilizer containing nitrapyrin inhibitor is responsible for slowing the activity of Nitrosomonas sp. bacteria down which oxidize ammonium to nitrite ions, thus, N-loss resulting from nitrate leaching can be reduced. Although prior studies have shown its effectiveness in the pre-sowing application in maize, considering that it disturbs the activity of Nitrosomonas bacteria which is the most intense between 25 °C and 30 °C, soil temperature may significantly influence the efficiency of nitrapyrin. Besides, nitrapyrin aims to enhance N-use efficiency in high N-demanding plants, such as maize, which demands N at the most during stalk elongation, which lays down the reason for its subsequent application. This study focuses on the efficiency of nitrapyrin at different soil temperatures and its impacts on the physiological development and productivity of maize. In a laboratory test, 10 °C, 15 °C, 20 °C, and 25 °C temperature soils were treated with nitrapyrin and change of nitrate content was monitored to observe the nitrification dynamic. Results show that as the soil temperature elevated, the inhibition efficiency increased. In a field experiment with maize, nitrapyrin was applied in 13 °C and 25 °C temperature soil. Results suggest the later treatment enhanced N-use efficiency, as, during the high N-demanding growth stage, more N-forms were available in the soil. This resulted in significantly higher relative chlorophyll concentration in the leaves and laboratory leaf analysis confirmed the prevention of N deficiency. Results of further measurements on parameters indicating biomass production such as root mass, stalk diameter, ear size, 1,000-kernel weight indicate that the nitrapyrin application should be timed later