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 4$\times$4 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 $m^{2}>q^{2}$, we find a physically acceptable time-dependent growing mode; thus the black hole is unstable. The extremal case $m^{2}=q^{2}$ 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 $\mathcal{N}=4,\, D=4$ 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 $\mathcal{N}=4,\, D=4$ 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 $J\neq 0$ 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: $2J/r^3$. 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