2,644 research outputs found
Multiply Warped Products with Non-Smooth Metrics
In this article we study manifolds with -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
-warping functions. We given the {\it{Ricci curvature}} in terms of ,
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 . This solution depends essentially on two
constants: the density and a parameter . 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 , 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 .
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 dimensions with a U(1) fibration over a -dimensional
base space . These solutions depend on two extra parameters, other
than the mass and the NUT charge, which are the electric charge and the
electric potential at infinity . We find that the form of metric is
sensitive to geometry of the base space, while the form of electromagnetic
field is independent of . 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 and the fact
that the horizon at 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 , there exist NUT solutions in
Gauss-Bonnet-Maxwell gravity. Indeed, we have non-extreme NUT solutions in
dimensions only when the -dimensional base space is chosen to be
. 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 . 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 dimensions. We
find that for all non-extremal NUT solutions of Einstein gravity having no
curvature singularity at , there exist NUT solutions in Gauss-Bonnet
gravity that contain these solutions in the limit that the Gauss-Bonnet
parameter 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 in the limit . Indeed,
we have non-extreme NUT solutions in dimensions with non-trivial
fibration only when the -dimensional base space is chosen to be
. 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 . 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 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 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
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