301 research outputs found
Accelerated Levi-Civita-Bertotti-Robinson Metric in D-Dimensions
A conformally flat accelerated charge metric is found in an arbitrary
dimension . It is a solution of the Einstein-Maxwell-null fluid with a
cosmological constant in dimensions. When the acceleration is zero
our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that
the charge loses its energy, for all dimensions, due to the acceleration.Comment: Latex File, 12 page
Closed timelike curves and geodesics of Godel-type metrics
It is shown explicitly that when the characteristic vector field that defines
a Godel-type metric is also a Killing vector, there always exist closed
timelike or null curves in spacetimes described by such a metric. For these
geometries, the geodesic curves are also shown to be characterized by a lower
dimensional Lorentz force equation for a charged point particle in the relevant
Riemannian background. Moreover, two explicit examples are given for which
timelike and null geodesics can never be closed.Comment: REVTeX 4, 12 pages, no figures; the Introduction has been rewritten,
some minor mistakes corrected, many references adde
Variable Coefficient Third Order KdV Type of Equations
We show that the integrable subclassess of a class of third order
non-autonomous equations are identical with the integrable subclassess of the
autonomous ones.Comment: Latex file , 15 page
Godel-type Metrics in Various Dimensions II: Inclusion of a Dilaton Field
This is the continuation of an earlier work where Godel-type metrics were
defined and used for producing new solutions in various dimensions. Here a
simplifying technical assumption is relaxed which, among other things,
basically amounts to introducing a dilaton field to the models considered. It
is explicitly shown that the conformally transformed Godel-type metrics can be
used in solving a rather general class of Einstein-Maxwell-dilaton-3-form field
theories in D >= 6 dimensions. All field equations can be reduced to a simple
"Maxwell equation" in the relevant (D-1)-dimensional Riemannian background due
to a neat construction that relates the matter fields. These tools are then
used in obtaining exact solutions to the bosonic parts of various supergravity
theories. It is shown that there is a wide range of suitable backgrounds that
can be used in producing solutions. For the specific case of (D-1)-dimensional
trivially flat Riemannian backgrounds, the D-dimensional generalizations of the
well known Majumdar-Papapetrou metrics of general relativity arise naturally.Comment: REVTeX4, 17 pp., no figures, a few clarifying remarks added and
grammatical errors correcte
Some Higher Dimensional Vacuum Solutions
We study an even dimensional manifold with a pseudo-Riemannian metric with arbitrary signature and arbitrary dimensions. We consider the Ricci flat equations and present a procedure to construct solutions to some higher (even) dimensional Ricci flat field equations from the four diemnsional Ricci flat metrics. When the four dimensional Ricci flat geometry correponds to a colliding gravitational vacuum spacetime our approach provides an exact solution to the vacuum Einstein field equations for colliding graviational plane waves in an (arbitrary) even dimensional spacetime. We give explicitly higher dimensional Szekeres metrics and study their singularity behaviors
On Non-Commutative Integrable Burgers Equations
We construct the recursion operators for the non-commutative Burgers
equations using their Lax operators. We investigate the existence of any
integrable mixed version of left- and right-handed Burgers equations on higher
symmetry grounds.Comment: 8 page
Boundary Value Problems For Integrable Equations Compatible With The Symmetry Algebra
Boundary value problems for integrable nonlinear partial differential
equations are considered from the symmetry point of view. Families of boundary
conditions compatible with the Harry-Dym, KdV and MKdV equations and the
Volterra chain are discussed. We also discuss the uniqueness of some of these
boundary conditions.Comment: 25 pages , Latex , no figure
A Note on Stress-Tensors, Conservation and Equations of Motion
Some unusual relations between stress tensors, conservation and equations of
motion are briefly reviewed.Comment: 4 pages. Invited contribution, A. Peres Festschrift, to be published
in Found. Phy
Killing Vector Fields in Three Dimensions: A Method to Solve Massive Gravity Field Equations
Killing vector fields in three dimensions play important role in the
construction of the related spacetime geometry. In this work we show that when
a three dimensional geometry admits a Killing vector field then the Ricci
tensor of the geometry is determined in terms of the Killing vector field and
its scalars. In this way we can generate all products and covariant derivatives
at any order of the ricci tensor. Using this property we give ways of solving
the field equations of Topologically Massive Gravity (TMG) and New Massive
Gravity (NMG) introduced recently. In particular when the scalars of the
Killing vector field (timelike, spacelike and null cases) are constants then
all three dimensional symmetric tensors of the geometry, the ricci and einstein
tensors, their covariant derivatives at all orders, their products of all
orders are completely determined by the Killing vector field and the metric.
Hence the corresponding three dimensional metrics are strong candidates of
solving all higher derivative gravitational field equations in three
dimensions.Comment: 25 pages, some changes made and some references added, to be
published in Classical and Quantum Gravit
Gauss-Bonnet Gravity with Scalar Field in Four Dimensions
We give all exact solutions of the Einstein-Gauss-Bonnet Field Equations
coupled with a scalar field in four dimensions under certain assumptions.Comment: Latex file, 7 page
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