We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be...

In extended new general relativity, which is formulated as a reduction of a Poincaré gauge theory of gravity whose gauge group is the covering group of the Poincaré group, we study the problem of whether the total energy-momentum, total angular momentum and total charge are equal to the corresponding quantities of the gravitational source. We examine this problem for charged axi-symmetric solut...

The confrontation between Einstein’s theory of gravitation and experiment is summarized. Although all current experimental data are compatible with General Relativity, the importance of pursuing the quest for possible deviations from Einstein’s theory is emphasized. ∗To appear in the Proceedings of the XIth International Congress of Mathematical Physics (Paris,July 1994)

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...

It is assumed that the radial propagation of light with respect to the naive coordinate system of the observer is uniform and isotropic and that the physical rate of propagation of light is the same for all observers. In accelerated frames of reference, these assumptions lead to the findings that the measured value of c is a function of the gravitational energy per unit mass (GEPUM) of the obse...

An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific conditions. A pseudo-complex Schwarzschild solution is constructed, which does not suffer any more by a singularity. The solution indicates a minimal radius for a he...