Related papers: About the S^3 Group-manifold Reduction of Einstein…
We present a geometrical unification theory in a Kaluza-Klein approach that achieve the geometrization of a generic gauge theory bosonic component. We show how it is possible to derive the gauge charge conservation from the invariance of…
For each simple symplectic triple system over the real numbers, the standard enveloping Lie algebra and the algebra of inner derivations of the triple provide a reductive pair related to a semi-Riemannian homogeneous manifold. It is proved…
An Einstein manifold in four dimensions has some configuration of $SU(2)_+$ Yang-Mills instantons and $SU(2)_-$ anti-instantons associated with it. This fact is based on the fundamental theorems that the four-dimensional Lorentz group…
Some time ago, the standard geometric framework of Einstein gravity was extended by gauging the Maxwell algebra as well as the so called AdS-Maxwell algebra. In this letter it is shown that the actions for these four-dimensional extended…
A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the "Vierbein" assuring local gauge invariance enters not as an independent dynamical field,…
We propose a reformulation of general relativity by making the Abelian decomposition of Einstein's theory. Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the Einstein's…
A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity --…
Dimensional reduction of (super-)gravity theories to 3 dimensions results in sigma models on coset spaces G/H, such as the E_8/SO(16) coset in the bosonic sector of 3 dimensional maximal supergravity. The reverse process, oxidation, is the…
This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any…
A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a…
The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
We present a detailed account of the isomonodromic quantization of dimensionally reduced Einstein gravity with two commuting Killing vectors. This theory constitutes an integrable ``midi-superspace" version of quantum gravity with…
We present three families of exact, cohomogeneity-one Einstein metrics in $(2n+2)$ dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of…
Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the gravitational connection (the gauge potential of Lorentz group) $\vGm_\mu$ into the restricted connection made of the potential…
We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives…
We provide a relatively self-contained introduction to the application of quantum spacetime and quantum Riemannian geometry to theoretical physics. Recent successes include calculation of the vacuum energy of spacetime curvature…
The dimensional reduction of a generic theory on a curved internal space such as a sphere does not admit a consistent truncation to a finite set of fields that includes the Yang-Mills gauge bosons of the isometry group. In rare cases, for…
In this paper the dynamic compactification in Lovelock gravity with a cubic term is studied. The ansatz will be of space-time where the three dimensional space and the extra dimensions are constant curvature manifolds with independent scale…
In this paper we prove weak L^{1,p} (and thus C^{\alpha}) compactness for the class of uniformly mean-convex Riemannian n-manifolds with boundary satisfying bounds on curvature quantities, diameter, and (n-1)-volume of the boundary. We…
We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of a…