20,090 research outputs found
A Twisting Electrovac Solution of Type II with the Cosmological Constant
An exact solution of the current-free Einstein-Maxwell equations with the
cosmological constant is presented. It is of Petrov type II, and its double
principal null vector is geodesic, shear-free, expanding, and twisting. The
solution contains five constants. Its electromagnetic field is non-null and
aligned. The solution admits only one Killing vector and includes, as special
cases, several known solutions.Comment: 4 pages, LaTeX 2e, no figures. The present (second) version,
identical to that published in General Relativity and Gravitation, is derived
from the first version by presenting the admitted Killing vector, and by
adding the last paragraph, two footnotes (here Footnotes 1 and 3), and two
references (here Refs. [3,4]
Curvature dependent lower bounds for the first eigenvalue of the Dirac operator
Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we
derive inequalities that involve a real parameter and join the eigenvalues of
the Dirac operator with curvature terms. The discussion of these inequalities
yields vanishing theorems for the kernel of the Dirac operator and lower
bounds for the spectrum of if the curvature satisfies certain conditions.Comment: Latex2e, 14p
Kaluza-Klein solitons reexamined
In (4 + 1) gravity the assumption that the five-dimensional metric is
independent of the fifth coordinate authorizes the extra dimension to be either
spacelike or timelike. As a consequence of this, the time coordinate and the
extra coordinate are interchangeable, which in turn allows the conception of
different scenarios in 4D from a single solution in 5D. In this paper, we make
a thorough investigation of all possible 4D scenarios, associated with this
interchange, for the well-known Kramer-Gross-Perry-Davidson-Owen set of
solutions. We show that there are {\it three} families of solutions with very
distinct geometrical and physical properties. They correspond to different sets
of values of the parameters which characterize the solutions in 5D. The
solutions of physical interest are identified on the basis of physical
requirements on the induced-matter in 4D. We find that only one family
satisfies these requirements; the other two violate the positivity of
mass-energy density. The "physical" solutions possess a lightlike singularity
which coincides with the horizon. The Schwarzschild black string solution as
well as the zero moment dipole solution of Gross and Perry are obtained in
different limits. These are analyzed in the context of Lake's geometrical
approach. We demonstrate that the parameters of the solutions in 5D are not
free, as previously considered. Instead, they are totally determined by
measurements in 4D. Namely, by the surface gravitational potential of the
astrophysical phenomena, like the Sun or other stars, modeled in Kaluza-Klein
theory. This is an important result which may help in observations for an
experimental/observational test of the theory.Comment: In V2 we include an Appendix, where we examine the conformal
approach. Minor changes at the beginning of section 2. In V3 more references
are added. Minor editorial changes in the Introduction and Conclusions
section
Maxwell Fields in Spacetimes Admitting Non-Null Killing Vectors
We consider source-free electromagnetic fields in spacetimes possessing a
non-null Killing vector field, . We assume further that the
electromagnetic field tensor, , is invariant under the action of the
isometry group induced by . It is proved that whenever the two
potentials associated with the electromagnetic field are functionally
independent the entire content of Maxwell's equations is equivalent to the
relation \n^aT_{ab}=0. Since this relation is implied by Einstein's equation
we argue that it is enough to solve merely Einstein's equation for these
electrovac spacetimes because the relevant equations of motion will be
satisfied automatically. It is also shown that for the exceptional case of
functionally related potentials \n^aT_{ab}=0 implies along with one of the
relevant equations of motion that the complementary equation concerning the
electromagnetic field is satisfied.Comment: 7 pages,PACS numbers: 04.20.Cv, 04.20.Me, 04.40.+
Geometrical properties of the trans-spherical solutions in higher dimensions
We investigate the geometrical properties of static vacuum -brane
solutions of Einstein gravity in dimensions, which have spherical
symmetry of orthogonal to the -directions and are invariant under
the translation along them. % The solutions are characterized by mass density
and tension densities. % The causal structure of the higher dimensional
solutions is essentially the same as that of the five dimensional ones. Namely,
a naked singularity appears for most solutions except for the Schwarzschild
black -brane and the Kaluza-Klein bubble. % We show that some important
geometric properties such as the area of and the total spatial volume
are characterized only by the three parameters such as the mass density, the
sum of tension densities and the sum of tension density squares rather than
individual tension densities. These geometric properties are analyzed in detail
in this parameter space and are compared with those of 5-dimensional case.Comment: 14 pages, 2 figures, Title change
Wigner Molecules in Nanostructures
The one-- and two-- particle densities of up to four interacting electrons
with spin, confined within a quasi one--dimensional ``quantum dot'' are
calculated by numerical diagonalization. The transition from a dense
homogeneous charge distribution to a dilute localized Wigner--type electron
arrangement is investigated. The influence of the long range part of the
Coulomb interaction is studied. When the interaction is exponentially cut off
the ``crystallized'' Wigner molecule is destroyed in favor of an inhomogeneous
charge distribution similar to a charge density wave .Comment: 10 pages (excl. Figures), Figures available on request LaTe
Binary black hole spacetimes with a helical Killing vector
Binary black hole spacetimes with a helical Killing vector, which are
discussed as an approximation for the early stage of a binary system, are
studied in a projection formalism. In this setting the four dimensional
Einstein equations are equivalent to a three dimensional gravitational theory
with a sigma model as the material source. The sigma
model is determined by a complex Ernst equation. 2+1 decompositions of the
3-metric are used to establish the field equations on the orbit space of the
Killing vector. The two Killing horizons of spherical topology which
characterize the black holes, the cylinder of light where the Killing vector
changes from timelike to spacelike, and infinity are singular points of the
equations. The horizon and the light cylinder are shown to be regular
singularities, i.e. the metric functions can be expanded in a formal power
series in the vicinity. The behavior of the metric at spatial infinity is
studied in terms of formal series solutions to the linearized Einstein
equations. It is shown that the spacetime is not asymptotically flat in the
strong sense to have a smooth null infinity under the assumption that the
metric tends asymptotically to the Minkowski metric. In this case the metric
functions have an oscillatory behavior in the radial coordinate in a
non-axisymmetric setting, the asymptotic multipoles are not defined. The
asymptotic behavior of the Weyl tensor near infinity shows that there is no
smooth null infinity.Comment: to be published in Phys. Rev. D, minor correction
Ring Wormholes in D-Dimensional Einstein and Dilaton Gravity
On the basis of exact solutions to the Einstein-Abelian gauge-dilaton
equations in -dimensional gravity, the properties of static axial
configurations are discussed. Solutions free of curvature singularities are
selected; they can be attributed to traversible wormholes with cosmic
string-like singularities at their necks. In the presence of an electromagnetic
field some of these wormholes are globally regular, the string-like singularity
being replaced by a set of twofold branching points. Consequences of wormhole
regularity and symmetry conditions are discussed. In particular, it is shown
that (i) regular, symmetric wormholes have necessarily positive masses as
viewed from both asymptotics and (ii) their characteristic length scale in the
big charge limit () is of the order of the ``classical radius"
.Comment: Latex file, 15 page
Solution generating with perfect fluids
We apply a technique, due to Stephani, for generating solutions of the
Einstein-perfect fluid equations. This technique is similar to the vacuum
solution generating techniques of Ehlers, Harrison, Geroch and others. We start
with a ``seed'' solution of the Einstein-perfect fluid equations with a Killing
vector. The seed solution must either have (i) a spacelike Killing vector and
equation of state P=rho or (ii) a timelike Killing vector and equation of state
rho+3P=0. The new solution generated by this technique then has the same
Killing vector and the same equation of state. We choose several simple seed
solutions with these equations of state and where the Killing vector has no
twist. The new solutions are twisting versions of the seed solutions
- …