Related papers: Space-time and G_2
We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation,…
A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can…
We construct a mathematically controlled correspondence between the electric and magnetic parts of the Weyl tensor in vacuum general relativity and the kinematics of a micropolar (Cosserat) elastic medium. In this framework, gravitational…
We show that the Teukolsky connection, which defines generalized wave operators governing the behavior of massless fields on Einstein spacetimes of Petrov type D, has its origin in a distinguished conformally and GHP covariant connection on…
Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string…
We study the class of vacuum (Ricci flat) six-dimensional spacetimes admitting a non-degenerate multiple Weyl aligned null direction l, thus being of Weyl type II or more special. Subject to an additional assumption on the asymptotic…
In the hybrid skyrmion in which an Anti-de Sitter bag is imbedded into the skyrmion configuration a S^{1}\times S^{2} membrane is lying on the compactified spatial infinity of the bag [H. Rosu, Nuovo Cimento B 108, 313 (1993)]. The…
In this paper, we analyse the well-posedness of the initial value formulation for particular kinds of geometric scalar-tensor theories of gravity, which are based on a Weyl integrable space-time. We will show that, within a frame-invariant…
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the…
We describe conditions under which a spacetime connection and a scaled Lorentzian metric define natural symplectic and Poisson structures on the tangent bundle of the Einstein spacetime.
The geometry of P, the bundle of null directions over an Einstein space-time, is studied. The full set of invariants of the natural G-structure on P is constructed using the Cartan method of equivalence. This leads to an extension of P…
We consider weakly regular Gowdy-symmetric spacetimes on T3 satisfying the Einstein-Euler equations of general relativity, and we solve the initial value problem when the initial data set has bounded variation, only, so that the…
We take a three dimensional Euclidian metric in toroidal coordinates and consider the corresponding Laplace equation. The simplest solution of this equation is taken. Based on this we build a Weyl space-time. This space-time is transformed…
A study of proper Weyl projective curvature collineations in FRW k=0 space-time is given using the rank of Weyl projective curvature matrix and direct integration techniques. It is shown that a very special class of the above space-time…
Based on a general formula due to R.Bryant, we work out the topological structure of the space of torsion-free $G_2$-structures generating the same associated Riemannian metric on a compact $7$-manifold. We also identify a corresponding Lie…
We investigate the existence of inhomogeneous exact solutions in Weyl Integrable theory with a matter source. In particular, we consider the existence of a dust fluid source while for the underlying geometry we assume a line element which…
In this article we apply the duality technique of R. Howe to study the structure of the Weyl algebra. We introduce a one-parameter family of ``ordering maps'', where by an ordering map we understand a vector space isomorphism of the…
We suggest that in the proper definition, Quantum Field Theories are quantum mechanical system which 'live' on the space of causal structures ${\cal C}$ of spacetime. That is, for any QFT a Hilbert space ${\cal H}$ on which local operators…
Consistency conditions for the local existence of massless spin 3/2 fields has been explored that the field equations for massless helicity 3/2 are consistent iff the space-time is Ricci-flat and that in Minkowski space-time the space of…
We consider self-consistent coupling of the recently introduced new class of Weyl-conformally invariant lightlike branes (WILL-branes) to D=4 Einstein-Maxwell system plus a D=4 three-index antisymmetric tensor gauge field. We find static…