Related papers: Null Killing Vector Dimensional Reduction and Gali…
It is an open question whether fluctuations at the Planck scale in a non-perturbative theory of quantum gravity behave in such a way that the resulting semi-classical geometry can be modelled by a space that admits (approximate) Killing…
Using a solution generating technique based on the symmetries of the dimensionally reduced Lagrangian we derive an exact solution of the Einstein-Maxwell-Dilaton field equations in five dimensions describing a system of two general…
In this paper we study the electromagnetic fields generated by a Killing vector field in vacuum space-times (Papapetrou fields). The motivation of this work is to provide new tools for the resolution of Maxwell's equations as well as for…
In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…
A new 5-dimensional Classical Unified Field Theory of Kaluza-Klein type is formulated using 2 separate scalar fields which are related in such a way as to make the 5-dimensional matter-geometry coupling parameter constant. It is shown that…
We propose a Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-splitting of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base…
Following steps analogous to classical Kaluza-Klein theory, we solve for the quantum Riemannian geometry on $C^\infty(M)\otimes M_2(\mathbb{C})$ in terms of classical Riemannian geometry on a smooth manifold $M$, a finite quantum geometry…
In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields - so-called hidden Killing vector fields - are constructed, which solve the Killing equation not globally, but only…
A complete set of wave solutions is given for the weak field in a Kaluza-Klein theory with degenerate metric. In the five-dimensional version of this theory electromagnetism is described by two vector fields, and there is a reflection…
In recent series of papers, we found an arbitrary dimensional, time-evolving and spatially-inhomogeneous solutions in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case the solution can be…
We explore spacetime torsion in a two-dimensional setting, wherein it corresponds to a vector field. Without invoking field equations of a particular gravitational theory, we develop visualization techniques for such torsion fields,…
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…
We obtain the vacuum spherical symmetric solutions for the gravitational sector of a (4+d)-dimensional Kaluza-Klein theory. In the various regions of parameter space, the solutions can describe either naked singularities or black-holes or…
Axially symmetric spacetimes are the only models for isolated systems with continuous symmetries that also include dynamics. For such systems, we review the reduction of the vacuum Einstein field equations to their most concise form by…
We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the $2$-dimensional Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a fundamental set of first-order scalar…
We employ a Kaluza-Klein dimensional reduction process on the action of the antisymmetric tensor field in five-dimensional space-time. The result is a joint field theory of four-dimensional antisymmetric and vector fields. We write the…
Considering a spacetime foliated by co-dimension-2 hypersurfaces, we find the conditions under which lower-dimensional symmetries of a base space can be lifted up to irreducible Killing tensors of the full spacetime. In this construction,…
We revisit the problem of extension of a Killing vector field in a spacetime which is solution to the Einstein-Maxwell equation. This extension has been proved to be unique in the case of a Killing vector field which is normal to a…
Let $(M,g)$ be a compact K\"ahler manifold and $f$ a positive smooth function such that its Hamiltonian vector field $K = J\mathrm{grad}_g f$ for the K\"ahler form $\omega_g$ is a holomorphic Killing vector field. We say that the pair…
The purpose of the present work is to extend the earlier results for asymptotically flat vacuum space-times to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically…