194 research outputs found
Colliding gravitational plane waves in dilaton gravity
Collision of plane waves in dilaton gravity theories and low energy limit of string theory is considered. The formulation of the the problem and some exact solutions are presented
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
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
Integrable nonlinear equations on a circle
The concept of integrable boundary value problems for soliton equations on
and is extended to bounded regions enclosed by
smooth curves. Classes of integrable boundary conditions on a circle for the
Toda lattice and its reductions are found.Comment: 23 page
Hydrodynamic type integrable equations on a segment and a half-line
The concept of integrable boundary conditions is applied to hydrodynamic type
systems. Examples of such boundary conditions for dispersionless Toda systems
are obtained. The close relation of integrable boundary conditions with
integrable reductions of multi-field systems is observed. The problem of
consistency of boundary conditions with the Hamiltonian formulation is
discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a
segment and a semi-line are presented
Static Einstein-Maxwell Solutions in 2+1 dimensions
We obtain the Einstein-Maxwell equations for (2+1)-dimensional static
space-time, which are invariant under the transformation
. It is shown that the
magnetic solution obtained with the help of the procedure used in
Ref.~\cite{Cataldo}, can be obtained from the static BTZ solution using an
appropriate transformation. Superpositions of a perfect fluid and an electric
or a magnetic field are separately studied and their corresponding solutions
found.Comment: 8 pages, LaTeX, no figures, to appear in Physical Review
Colliding Wave Solutions in a Symmetric Non-metric Theory
A method is given to generate the non-linear interaction (collision) of
linearly polarized gravity coupled torsion waves in a non-metric theory.
Explicit examples are given in which strong mutual focussing of gravitational
waves containing impulsive and shock components coupled with torsion waves does
not result in a curvature singularity. However, the collision of purely torsion
waves displays a curvature singularity in the region of interaction.Comment: 16 pages, 1 ps figure, It will appear in Int. Jour. of Theor. Physic
All Static Circularly Symmetric Perfect Fluid Solutions of 2+1 Gravity
Via a straightforward integration of the Einstein equations with cosmological
constant, all static circularly symmetric perfect fluid 2+1 solutions are
derived. The structural functions of the metric depend on the energy density,
which remains in general arbitrary. Spacetimes for fluids fulfilling linear and
polytropic state equations are explicitly derived; they describe, among others,
stiff matter, monatomic and diatomic ideal gases, nonrelativistic degenerate
fermions, incoherent and pure radiation. As a by--product, we demonstrate the
uniqueness of the constant energy density perfect fluid within the studied
class of metrics. A full similarity of the perfect fluid solutions with
constant energy density of the 2+1 and 3+1 gravities is established.Comment: revtex4, 8 page
Accelerated Born-Infeld Metrics in Kerr-Schild Geometry
We consider Einstein Born-Infeld theory with a null fluid in Kerr-Schild
Geometry. We find accelerated charge solutions of this theory. Our solutions
reduce to the Plebanski solution when the acceleration vanishes and to the
Bonnor-Vaidya solution as the Born-Infeld parameter b goes to infinity. We also
give the explicit form of the energy flux formula due to the acceleration of
the charged sources.Comment: Latex file (12 pp
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