Related papers: The General Relativity of Two Properties
We develop the general relativity of extended spacetime-property for describing events including their properties. The anticommuting nature of property coordinates, augmenting space-time $({\bf x},t)$, allows for the natural emergence of…
We determine the coefficients of the terms multiplying the gauge fields, gravitational field and cosmological term in a scheme whereby properties are characterized by $N$ anticommuting scalar Grassmann variables. We do this for general $N$,…
By attaching three anticommuting Lorentz scalar (colour) property coordinates to space-time, with an appropriate extended metric, we unify gravity with chromodynamics: gauge transformations then just correspond to coordinate transformations…
The careful analysis of the duality properties of Riemann's curvature tensor points to possibility of extension of Einstein's General Relativity to the nonabelian Yang-Mills theory. The motion equations of the theory are Yang-Mills'…
By attaching five (complex) anticommuting property coordinates to the four (real) commuting space-time ones, it is possible to accommodate all the known fundamental particles in their three generations. A general relativistic extension to…
A ghost-free theory of gravity with two dynamical metrics both coupled to matter is shown to be consistent and viable. Its cosmological implications are studied, and the models, in particular in the context of partially massless gravity,…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its…
We describe a geometrical way to unify gravity with the other natural forces by adding fermionic Lorentz scalar variables, characterising attribute, or property, to space-time location. [With five such properties one can accommodate all…
A non-abelian generalisation of a theory of gravity coupled to a 2-form gauge field and a dilaton is found, in which the metric and 3-form field strength are Lie algebra-valued. In the abelian limit, the curvature with torsion is self-dual…
By gauging the Maxwell spacetime algebra the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six fourvector fields A_\mu^{ab}(x) associated with the six abelian tensorial charges in the…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
We introduce a dual lifting of unified gauge theories, the first characterized by the isotopies, which are axiom- preserving maps into broader structures with positive-definite generalized units used for the representation of matter under…
We develop a novel approach to gravity in which gravity is described by a matrix-valued symmetric two-tensor field and construct an invariant functional that reduces to the standard Einstein-Hilbert action in the commutative limit. We also…
The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter is discovered an exceptional class which is consistent with a vanishing affine connection. Based on…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
Noncommutative geometric construction of gravity in the two sheeted spacetime can be viewed as a discretized version of a Kaluza-Klein theory. In this paper, we show that it is possible to incorporate the nonabelian gauge fields in the same…
We present a simple unifying gauge theoretical formulation of gravitational theories in two dimensional spacetime. This formulation includes the effects of a novel matter-gravity coupling which leads to an extended de Sitter symmetry…
We propose a canonical relation between gravity and space-time noncommutativity.
We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric.…