According to an a-temporal quantum-gravity space theory recently suggested, the gravitational space turns out to have a wave and granular nature, and its properties derive from two fundamental physical quantities: the density of cosmic space (intended as the physical quantity which is linked with the amount of matter present in the region under consideration), and a quantum number indicating a sort of ‘rotation-orientation’ of each point of the gravitational space. In the mathematical formalism of this approach, which is based on a generalized Klein-Gordon equation and a generalized Fiscaletti-Dirac equation for the density of cosmic space, important results as regards the curvature and granular structure of space can be obtained. Moreover, the generalized Fiscaletti-Dirac equation for the density of cosmic space suggests a new interesting key of reading of the Klein paradox. In the second part of this paper, a generalized Fiscaletti-Dirac equation for the density of cosmic space with electromagnetic interaction is introduced and its perspectives in the treatment of the curvature of space are analyzed.

The a-temporal quantum-gravity space theory is based on the following foundational ideas, which can be considered as the postulates of this model (Fiscaletti, 2010a and 2010b):

• The gravitational space is characterized by two levels of description: a universal ‘cosmic space’ which is a primordial pre-quantum pre-space, and a quantum-gravity space which emerges from the cosmic space and exhibits a wave nature.
  
• The cosmic space is defined in terms of two fundamental quantities: the density of cosmic space (which is linked with the amount of matter present in the region under consideration) and a quantum number indicating a sort of ‘rotation-orientation’ of each point of the gravitational space. The density of cosmic space associated with a material object of mass m in the points situated at distance r from the center of this object is defined by the relation

Physics Journal, Electrical Transport Properties, Transmission Electron Microscopy, Magnetotransport Data, Antiferromagnetic Semiconductors, Chemical Precipitation Method, Nanocrystalline Manganites, Perovskite Structure, Citrate-gel Method, Polycrystalline Perovskite Material, Debye Scherrer Formula.