58 research outputs found
Developed Adomian method for quadratic Kaluza-Klein relativity
We develop and modify the Adomian decomposition method (ADecM) to work for a
new type of nonlinear matrix differential equations (MDE's) which arise in
general relativity (GR) and possibly in other applications. The approach
consists in modifying both the ADecM linear operator with highest order
derivative and ADecM polynomials. We specialize in the case of a 44
nonlinear MDE along with a scalar one describing stationary cylindrically
symmetric metrics in quadratic 5-dimensional GR, derive some of their
properties using ADecM and construct the \textit{most general unique power
series solutions}. However, because of the constraint imposed on the MDE by the
scalar one, the series solutions terminate in closed forms exhausting all
possible solutions.Comment: 17 pages (minor changes in reference [30]
Quadratic superconducting cosmic strings revisited
It has been shown that 5-dimensional general relativity action extended by
appropriate quadratic terms admits a singular superconducting cosmic string
solution. We search for cosmic strings endowed with similar and extended
physical properties by directly integrating the non-linear matrix field
equations thus avoiding the perturbative approach by which we constructed the
above-mentioned \textsl{exact} solution. The most general superconducting
cosmic string, subject to some constraints, will be derived and shown to be
mathematically \textsl{unique} up to linear coordinate transformations mixing
its Killing vectors. The most general solution, however, is not globally
equivalent to the old one due to the existence of Killing vectors with closed
orbits.Comment: 6 page
A theorem on the photographic process in Special Relativity. The train paradox revisited
The purpose of this letter is to show, on the one hand, how the so-called
train paradox could be resolved directly without appealing to non-linear
Lorentz transformations. The resolution is established in the most general case
of curvilinear motion with a variable speed train. On the other hand, we
formulate a theorem on the photographic process of two moving objects with
relativistic effects.Comment: 7 pages, 1 figur
Instability of two-dimensional heterotic stringy black holes
We solve the eigenvalue problem of general relativity for the case of charged
black holes in two-dimensional heterotic string theory, derived by McGuigan et
al. For the case of , we find a physically acceptable
time-dependent growing mode; thus the black hole is unstable. The extremal case
is stable.Comment: 11 pages, LaTe
Classification of BPS instantons in N=4 D=4 supergravity
This talk is based on the recent work in collaboration with M.
Azreg-A\"{\i}nou and G. Cl\'ement devoted to extremal instantons in the
one-vector truncation of the Euclidean theory. Extremal
solutions satisfying the no-force condition can be associated with null
geodesic curves in the homogeneous target space of the three-dimensional sigma
model arising in toroidal reduction of the four-dimensional theory. Here we
(preliminarily) discuss the case of two vector fields sufficient to find all
relevant metrics in the full theory. Classification of
instanton solutions is given along the following lines. The first is their
possible asymptotic structure: asymptotically locally flat (ALF),
asymptotically locally Euclidean (ALE) and ALF or ALE with the dilaton growing
at infinity. The second is the algebraic characterization of matrix generators
according to their rank and the nature of the charge vectors in an associated
Lorentzian space. Finally, solutions are distinguished by the number of
independent harmonic functions with unequal charges (up to four).Comment: Submitted to Proceedings of "Quantum Theory and Symmetries" (QTS-7),
Prague, August 7-13, 201
Rotation and twist regular modes for trapped ghosts
A parameter-independent notion of stationary slow motion is formulated then
applied to the case of stationary rotation of massless trapped ghosts. The
excitations correspond to a rotation mode with angular momentum and
twist modes. It is found that the rotation mode, which has no parity, causes
excess in the angular velocity of dragged distant coordinate frames in one
sheet of the wormhole while in the other sheet the angular velocity of the
ghosts is that of rotating stars: . As to the twist modes, which all
have parity, they cause excess in the angular velocity of one of the throat's
poles with respect to the other.Comment: 11 pages, 3 figures; General Relativity and Gravitation - 201
Dyonic Wormholes in 5D Kaluza-Klein Theory
New spherically symmetric dyonic solutions, describing a wormhole-like class
of spacetime configurations in five-dimensional Kaluza-Klein theory, are given
in an explicit form. For this type of solution the electric and magnetic fields
cause a significantly different global structure. For the electric dominated
case, the solution is everywhere regular but, when the magnetic strength
overcomes the electric contribution, the mouths of the wormhole become singular
points. When the electric and magnetic charge parameters are identical, the
throats ``degenerate'' and the solution reduces to the trivial embedding of the
four-dimensional massless Reissner-Nordstr{\"o}m black hole solution. In
addition, their counterparts in eleven-dimensional supergravity are constructed
by a non-trivial uplifting.Comment: Revised version to appear in Class. Quant. Gra
- …