General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field and to the geodesic equations that describe light propagation and the motion of particles on the background. But open questions remain, including: what is the scale on which matter and geometry are dynamically coupled in the Einstein equation...

A historical account of Einstein’s Fernparallelismus approach towards a unified field theory of gravitation and electromagnetism is given. In this theory, a spacetime characterized by a curvature-free connection in conjunction with a metric tensor field, both defined in terms of a dynamical tetrad field, is investigated. The approach was pursued by Einstein in a number of publications that appe...

We present an analysis of a n-dimensional vacuum Einstein field equations in which 4-dimensional space-time with is described by a Friedmann Robertson-Walker (FRW) metric and that of the extra dimensions by a Kasner type Euclidean metric. The field equations are interpreted as four dimensional Einstein equations with effective matter properties. We obtain solutions for the cases when the effect...

It is argued that, in order for the gravitational field to be propagated as a wave, it is necessary for it to satisfy a further set of field equations, in addition to those of Einstein and Hilbert, and these equations mean there is a preferred coordinate frame, called the Global Inertial Frame, giving rise to a unique metric . The implication is that a true gravitational field is not compatible...

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, i.e., at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point...

The generalized Einstein Maxwell field equations which arise from a truncated bosonic part of the low energy string gravity effective action in four dimensions (the so called Einstein-Maxwell axion dilaton theory) are considered. The integrable structure of these field equations for D = 4 space-times with two commuting isometries is elucidated. We express the dynamical part of the reduced equat...

We construct thin shell Lorentzian wormholes in higher dimensional Einstein-Maxwell theory applying the ' Cut and Paste ' technique proposed by Visser. The linearized stability is analyzed under radial perturbations around some assumed higher dimensional spherically symmetric static solution of the Einstein field equations in presence of Electromagnetic field. We determine the total amount of e...