Multiply Warped Products with Non-Smooth Metrics

In this article we study manifolds with $C^{0}$-metrics and properties of Lorentzian multiply warped products. We represent the interior Schwarzschild space-time as a multiply warped product space-time with warping functions and we also investigate the curvature of a multiply warped product with $C^0$-warping functions. We given the {\it{Ricci curvature}} in terms of $f_1$, $f_2$ for the multiply warped products of the form $M=(0,\ 2m)\times_{f_1}R^1\times_{f_2} S^2$.Comment: LaTeX, 7 page

Infinite slabs and other weird plane symmetric space-times with constant positive density

We present the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$. This solution depends essentially on two constants: the density $\rho$ and a parameter $\kappa$. We show that this space-time finishes down below at an inner singularity at finite depth. We match this solution to the vacuum one and compute the external gravitational field in terms of slab's parameters. Depending on the value of $\kappa$, these slabs can be attractive, repulsive or neutral. In the first case, the space-time also finishes up above at another singularity. In the other cases, they turn out to be semi-infinite and asymptotically flat when $z\to\infty$. We also find solutions consisting of joining an attractive slab and a repulsive one, and two neutral ones. We also discuss how to assemble a "gravitational capacitor" by inserting a slice of vacuum between two such slabs.Comment: 8 page

Taub-NUT/Bolt Black Holes in Gauss-Bonnet-Maxwell Gravity

We present a class of higher dimensional solutions to Gauss-Bonnet-Maxwell equations in $2k+2$ dimensions with a U(1) fibration over a $2k$-dimensional base space $\mathcal{B}$. These solutions depend on two extra parameters, other than the mass and the NUT charge, which are the electric charge $q$ and the electric potential at infinity $V$. We find that the form of metric is sensitive to geometry of the base space, while the form of electromagnetic field is independent of $\mathcal{B}$. We investigate the existence of Taub-NUT/bolt solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two other conditions. These two extra conditions come from the regularity of vector potential at $r=N$ and the fact that the horizon at $r=N$ should be the outer horizon of the black hole. We find that for all non-extremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet-Maxwell gravity. Indeed, we have non-extreme NUT solutions in $2+2k$ dimensions only when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet-Maxwell gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet-Maxwell gravity with any base space. The only case for which one does not have black hole solutions is in the absence of a cosmological term with zero curvature base space.Comment: 23 pages, 3 figures, typos fixed, a few references adde

NUT-Charged Black Holes in Gauss-Bonnet Gravity

We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in $d$ dimensions. We find that for all non-extremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter $\alpha$ goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield non-extremal NUT solutions to Einstein gravity having a curvature singularity at $r=N$ in the limit $$. Indeed, we have non-extreme NUT solutions in $2+2k$ dimensions with non-trivial fibration only when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.Comment: 20 pages, referrence added, a few typos correcte

Different Melting Behavior in Pentane and Heptane Monolayers on Graphite; Molecular Dynamics Simulations

Molecular dynamics simulations are utilized to study the melting transition in pentane (C5H12) and heptane (C7H16), physisorbed onto the basal plane of graphite at near-monolayer coverages. Through use of the newest, optimized version of the anisotropic united-atom model (AUA4) to simulate both systems at two separate coverages, this study provides evidence that the melting transition for pentane and heptane monolayers are significantly different. Specifically, this study proposes a very rapid transition from the solid crystalline rectangular-centered (RC) phase to a fluid phase in pentane monolayers, whereas heptane monolayers exhibit a slower transition that involves a more gradual loss of RC order in the solid-fluid phase transition. Through a study of the melting behavior, encompassing variations where the formation of gauche defects in the alkyl chains are eliminated, this study proposes that this gradual melting behavior for heptane monolayers is a result of less orientational mobility of the heptane molecules in the solid RC phase, as compared to the pentane molecules. This idea is supported through a study of a nonane monolayer, which gives the gradual melting signature that heptane monolayers also seem to indicate. The results of this work are compared to previous experiment over pentane and heptane monolayers, and are found to be in good agreement

Distributional energy momentum tensor of the extended Kerr geometry

We generalize previous work on the energy-momentum tensor-distribution of the Kerr geometry by extending the manifold structure into the negative mass region. Since the extension of the flat part of the Kerr-Schild decomposition from one sheet to the double cover develops a singularity at the branch surface we have to take its non-smoothness into account. It is however possible to find a geometry within the generalized Kerr-Schild class that is in the Colombeau-sense associated to the maximally analytic Kerr-metric.Comment: 12 pages, latex2e, amslatex and epsf macro

Determination of the mosaic angle distribution of Grafoil platelets using continuous-wave NMR spectra

We described details of a method to estimate with good accuracy the mosaic angle distributions of microcrystallites (platelets) in exfoliated graphite like Grafoil which is commonly used as an adsorption substrate for helium thin films. The method is based on analysis of resonance field shifts in continuous-wave (CW) NMR spectra of $^{3}$He ferromagnetic monolayers making use of the large nuclear polarization of the adsorbate itself. The mosaic angle distribution of a Grafoil substrate analyzed in this way can be well fitted to a gaussian form with a $27.5\pm2.5$ deg spread. This distribution is quite different from the previous estimation based on neutron scattering data which showed an unrealistically large isotropic powder-like component.Comment: 6 pages, 5 figure

Study of quasi-optical circuit techniques in varactor multipliers

Quasi-optical circuit techniques in varactor multiplier

Self-enforcing cooperation via strategic investment

We investigate how, in a situation with two players in which noncooperation is the only equilibrium, cooperation can be achieved via costly investment. We find that in the resulting equilibria, cooperation is an all-or-nothing outcome, that is, either there is full cooperation by both players, or no cooperation at all. The cost of investment is unrelated to the degree of cooperation that is ultimately achieved, unless the cost is too high, in which case investment cannot in any degree overcome the disincentive to cooperate. Moreover, the positive externalities that players have on each other in the course of play, although they affect investment, are ultimately irrelevant to the degree of cooperation achieved. We view our model as an explanation for the formation and stable existence of business alliances, where the players are firms forming a partnership defined and sustained by contractual agreements, but which is short of a merger or acquisition