Accounting for exotic matter and the extreme radial tension in Morris–Thorne wormholes of embedding class one

The embedding of a curved spacetime in a higher-dimensional flat spacetime has continued to be a topic of interest in the general theory of relativity, as exemplified by the induced-matter theory. This paper deals with spacetimes of embedding class one, i.e., spacetimes that can be embedded in a five-dimensional flat spacetime. Einstein’s theory allows the fifth dimension to be either spacelike or timelike. By assuming the latter, this paper addresses two fundamental issues concerning Morris–Thorne wormholes, the origin of exotic matter and the frequently inexplicable enormous radial tension at the throat.

The Modern Induced Matter Approach of General Relativity for Quantum Mechanics

Wesson and his co-workers developed so-called space-time-matter theory (5D-STM) as a generalization of Kaluza-Klein theory, where the extra-dimension in the 5D space-time is no more compacted, but keeping extended in a macroscopic scale to describe the properties of matter in 4D physics. In a trend of 5D-STM approach (or the induced-matter theory), following a bi-cylindrical model of geometrical dynamics, a recent study has shown that the higher 6D-dimensional gravitational equation leads to bi-geodesic description in an extended timespace symmetry which fits Hubble expansion in a ”microscopic” cosmological model. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles. The 4D-embedded dual solutions of the higher dimensional gravitational equation could shed light on origin of physical reality in quantum mechanics, which is to compare with the achievements of the 5D-STM theory.

Quantized gravito-magnetic charges from WIMT: cosmological consequences

Using the formalism of Weitzenböck induced matter theory (WIMT) we calculate the gravito-magnetic charge on a topological string, which is induced through a foliation on a five-dimensional (5D) gravito-electromagnetic vacuum defined on a 5D Ricci-flat metric, which produces symmetry breaking on an axis. We obtain the resonant result that the quantized charges are induced on the effective four-dimensional hypersurface. This quantization describes the behavior of a test gravito-electric charge in the vicinity of a point gravito-magnetic monopole, both geometrically induced from a 5D vacuum. We demonstrate how gravito-magnetic monopoles would decrease exponentially during the inflationary expansion of the universe.

Gravity and induced matter on nearly Kähler manifolds

We show that the conservation of energy–momentum tensor of a gravitational model with Einstein–Hilbert like action on a nearly Kähler manifold with the scalar curvature of a curvature-like tensor, is consistent with the nearly Kähler properties. In this way, the nearly Kähler structure is automatically manifested in the action as a induced matter field. As an example of nearly Kähler manifold, we consider the group manifold of R×II ×S3×S3 on which we identify a nearly Kähler structure and solve the Einstein equations to interpret the model. It is shown that the nearly Kähler structure in this example is capable of alleviating the well known fine tuning problem of the cosmological constant. Moreover, this structure may be considered as a potential candidate for dark energy.