447 research outputs found
Godel-Type Metrics in Various Dimensions
Godel-type metrics are introduced and used in producing charged dust
solutions in various dimensions. The key ingredient is a (D-1)-dimensional
Riemannian geometry which is then employed in constructing solutions to the
Einstein-Maxwell field equations with a dust distribution in D dimensions. The
only essential field equation in the procedure turns out to be the source-free
Maxwell's equation in the relevant background. Similarly the geodesics of this
type of metric are described by the Lorentz force equation for a charged
particle in the lower dimensional geometry. It is explicitly shown with several
examples that Godel-type metrics can be used in obtaining exact solutions to
various supergravity theories and in constructing spacetimes that contain both
closed timelike and closed null curves and that contain neither of these. Among
the solutions that can be established using non-flat backgrounds, such as the
Tangherlini metrics in (D-1)-dimensions, there exists a class which can be
interpreted as describing black-hole-type objects in a Godel-like universe.Comment: REVTeX4, 19 pp., no figures, improved and shortened version, note the
slight change in the title [accepted for publication in Classical and Quantum
Gravity
Travelling Wave Solution of Degenerate Coupled KdV Equations
Cataloged from PDF version of article.We give a detailed study of the traveling wave solutions of (l = 2) Kaup-Boussinesq type of coupled KdV equations. Depending upon the zeros of a fourth degree polynomial, we have cases where there exist no nontrivial real solutions, cases where asymptotically decaying to a constant solitary wave solutions, and cases where there are periodic solutions. All such possible solutions are given explicitly in the form of Jacobi elliptic functions. Graphs of some exact solutions in solitary wave and periodic shapes are exhibited. Extension of our study to the cases l = 3 and l = 4 are also mentioned. (C) 2014 AIP Publishing LLC
Exact static solutions in four dimensional Einstein-Maxwell-Dilaton gravity
Classes of exact static solutions in four-dimensional
Einstein-Maxwell-Dilaton gravity are found. Besides of the well-known solutions
previously found in the literature, new solutions are presented.It's shown that
spherically symmetric solutions, except the case of charged dilaton black hole,
represent globally naked strong curvature singularities.Comment: 8 pages, late
Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations
Cataloged from PDF version of article.Using the formulation of the immersion of a two-dimensional surface into the three-dimensional Euclidean space proposed recently, a mapping from each symmetry of integrable equations to surfaces in ℝ3 can be established. We show that among these surfaces the sphere plays a unique role. Indeed, under the rigid SU(2) rotations all integrable equations are mapped to a sphere. Furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine-Gordon equation are homeomorphic to a sphere. We also find some new Weingarten surfaces arising from the deformations of the modified Kurteweg-de Vries and of the nonlinear Schrödinger equations. Surfaces can also be associated with the motion of curves. We study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity. © 2000 American Institute of Physics
Type IIB Colliding Plane Waves
Four-dimensional colliding plane wave (CPW) solutions have played an
important role in understanding the classical non-linearities of Einstein's
equations. In this note, we investigate CPW solutions in --dimensional
Einstein gravity with a -form flux. By using an isomorphism with the
four-dimensional problem, we construct exact solutions analogous to the
Szekeres vacuum solution in four dimensions. The higher-dimensional versions of
the Khan-Penrose and Bell-Szekeres CPW solutions are studied perturbatively in
the vicinity of the light-cone. We find that under small perturbations, a
curvature singularity is generically produced, leading to both space-like and
time-like singularities. For , our results pertain to the collision of two
ten-dimensional type IIB Blau - Figueroa o'Farrill - Hull - Papadopoulos plane
waves.Comment: 20+10 pages, 2 figures, uses JHEP3.cls; v2: refs [3,10,22] corrected,
remark added below (3.9) on inexistence of conformally flat CPW in our
ansatz, final version to appear in JHE
Colliding Plane Waves in String Theory
We construct colliding plane wave solutions in higher dimensional gravity
theory with dilaton and higher form flux, which appears naturally in the low
energy theory of string theory. Especially, the role of the junction condition
in constructing the solutions is emphasized. Our results not only include the
previously known CPW solutions, but also provide a wide class of new solutions
that is not known in the literature before. We find that late time curvature
singularity is always developed for the solutions we obtained in this paper.
This supports the generalized version of Tipler's theorem in higher dimensional
supergravity.Comment: latex, 25 pages, 1 figur
On the naming of innovation districts
Name plays a fundamental role in defining and differentiating a company within a category. In this paper we identify how the leaders of 7 innovation districts (22@Barcelona, Ann Arbor Spark, EECi, Porto Digital, Ruta N – Medellín, SK-Skolkovo and TusPark) understand the construction of the names of their innovation districts. We take an inductive approach utilizing two types of data: exploring the innovation district directors' understanding through direct semi-structured interviews and analyzing secondary data consisting of website and brochures. We show how innovation district leaders use more than one classification name for their organization and that these names either tend towards a more strategic or institutional posture. We contribute by extending existing naming theory to include innovation districts, a complex organization composed by actors of the Triple Helix. We also contribute by providing managerial guidance to assist in understanding the importance of the role of their organization's name in long-term positioning
Behaviour of Magnetic Tubes in Neutron Star's Interior
It is found from Maxwell's equations that the magnetic field lines are good
analogues of relativistic strings. It is shown that the super-conducting
current in the neutron star's interior causes local rotation of magnetic flux
tubes carrying quantized flux.Comment: 6 pages, no figure
Thin static charged dust Majumdar-Papapetrou shells with high symmetry in D >= 4
We present a systematical study of static D >= 4 space-times of high symmetry
with the matter source being a thin charged dust hypersurface shell. The shell
manifold is assumed to have the following structure S_(beta) X R^(D-2-beta),
beta (in the interval ) is dimension of a sphere S_(beta). In case
of (beta) = 0, we assume that there are two parallel hyper-plane shells instead
of only one. The space-time has Majumdar-Papapetrou form and it inherits the
symmetries of the shell manifold - it is invariant under both rotations of the
S_(beta) and translations along R^(D-2-beta). We find a general solution to the
Einstein-Maxwell equations with a given shell. Then, we examine some flat
interior solutions with special attention paid to D = 4. A connection to D = 4
non-relativistic theory is pointed out. We also comment on a straightforward
generalisation to the case of Kastor-Traschen space-time, i.e. adding a
non-negative cosmological constant to the charged dust matter source.Comment: Accepted in Int. J. Theor. Phy
Chiral models in dilaton-Maxwell gravity
We study symmetry properties of the Einstein-Maxwell theory nonminimaly
coupled to the dilaton field. We consider a static case with pure electric
(magnetic) Maxwell field and show that the resulting system becomes a nonlinear
sigma-model wich possesses a chiral representation. We construct the
corresponding chiral matrix and establish a representation which is related to
the pair of Ernst-like potentials. These potentials are used for separation of
the symmetry group into the gauge and nongauge (charging) sectors. New
variables, which linearize the action of charging symmetries, are also
established; a solution generation technique based on the use of charging
symmetries is formulated. This technique is used for generation of the
elecricaly (magneticaly) charged dilatonic fields from the static General
Relativity ones.Comment: 9 pages in LaTex; published in Gen. Rel. Grav. 32 (2000) pp 1389-139
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