Local diffeomorphisms and smooth embeddings to gravitational field II: spherical symmetry and their breaking in the space-time

Abstract

Consequences of the diffeomorphisms induced by K− invariant connections of the space of 1-forms of certain endomorphisms defined over a Lie algebra that is isomorphic to the tangent space seated in the identity element, of homogeneous spaces G/K⊂G/H , are analized. The images of these diffeomorphisms in G/H , are 2-form of curvatures that can be induced to each class of the G/K . Then using the K− invariant connection of this homogeneous space, the curvature can be determined as a regular representation that admits a finite discomposing of irreducible sub-representations of finite type, accord with the generalizing in dimensions of the Gauss-Bonnet theorem and the generalized Radon transform to obtain curvature through of co-cycles of the image of the corresponding space. Such irreducible sub-representations will be isotopic components of the certain smoothly embedded image in a manifold modelled this last, by a generalized function space. Likewise, through these realizations we have the curvature integrals as dual case of their field equations. Finally, using the complex Riemannian structure of our model of the space-time, and the K− invariant G− structure of the orbits used to obtain curvature, are obtained as consequences of the diffeomorphisms the field equations to the energy-matter tensor density in each case of the gravitational field. Of this manner, is determined their energy-mass tensor density as an integral which represents the energy spectra of the curvature when this is obtained in duality to the homogeneous field equations to the Riemann tensor Rμν−12gμν R.