Space Time Matter Theory Research Articles

Hawking radiation of 5D Ricci-flat black hole

In this paper, we investigate the properties of a five-dimensional Ricci-flat black hole within the framework of the Space–Time–Matter theory. By employing the Klein–Gordon equation, we derive the wave function equations for both the mass dimensional coordinate and the radial dimensional coordinate. We present the analytical solutions for the wave function on the mass dimensional coordinate under two distinct scenarios. Remarkably, we observe the absence of quantum effects on the mass dimensional coordinate, which aligns with the absence of a barrier in the wave function equation. For the radial component, we employ the B-spline method to numerically solve its wave function. Our findings reveal the existence of Hawking radiation between the event horizon and the cosmological horizon, with the transmission and reflection probabilities being determined by the presence of a barrier. Furthermore, we discover a significantly higher probability of particle detection near the cosmological horizon, while the probability near the event horizon approaches zero.

Noncompactified Kaluza–Klein Gravity

We present a brief description of noncompactified higher-dimensional theories from the perspective of general relativity. More concretely, the Space–Time–Matter theory, or Induced Matter theory, and the reduction procedure used to construct the modified Brans–Dicke theory and the modified Sáez–Ballester theory are briefly explained. Finally, we apply the latter to the Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological models in arbitrary dimensions and analyze the corresponding solutions.

A Time–Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time–space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein–Gordon–Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space–time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space–time–matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.

Cosmic acceleration from varying masses in five dimensions

Much effort has been made in trying to solve or at least evade the inconsistencies that emerge from general relativity as the framework for a cosmological model. The extradimensional models rise as superb possibilities in this regard. In this work, I present cosmological solutions for Wesson’s space–time–matter theory of gravity. A relation between mass variation at cosmological scales and the expansion velocity of the universe is obtained. Such a relation yields novel features on space–time–matter theory of gravity, which are carefully discussed.

$$4D$$ 4 D Einstein equations in a $$5D$$ 5 D general Kaluza–Klein space

Based on the new point of view on space–time–matter theory developed in our paper (Bejancu, Gen Rel Grav, 2013), we obtain the $$4D$$ Einstein equations in a general $$5D$$ Kaluza–Klein space with electromagnetic potentials. In particular, we recover the $$4D$$ Einstein equations obtained by Wesson and Ponce de Leon (J Math Phys 33:3883, 1992) in case the electromagnetic potentials vanish identically on $$\bar{M}$$ . The Riemannian horizontal connection and the $$4D$$ tensor calculus on $$\bar{M}$$ , are the main tools in the study.

$$4D$$ 4 D Equations of motion and fifth force in a $$5D$$ 5 D general Kaluza–Klein space

In this paper we present a new point of view on space–time–matter (STM) theory. First, some weak points from earlier research papers on STM theory are presented. Then, we obtain in a covariant form the fully general \(4D\) equations of motion for STM theory. This enables us to classify the \(5D\) motions and to give a new definition of the fifth force in \(4D\) physics.

EQUATIONS OF MOTION FOR SPACE-TIME-MATTER THEORY

The purpose of this paper is to present, in a covariant form and in their full generality, the equations of motion for space-time-matter (STM) theory. The whole study is based on the new approach of STM theory developed in our first paper [1] of this series. We show that the theory of geodesics in a general Kaluza–Klein space is best presented and explained by splitting the set of all geodesics into horizontal and non-horizontal geodesics. It is noteworthy that the horizontal geodesics (respectively, non-horizontal geodesics) project on the base manifold on motions which generalize the motions from general relativity theory (respectively, motions from Lorentz force equations).

The geometry of space–time–matter

We formulate a global, differential geometric structure for the space–time–matter theory introduced by Wesson and coworkers. In addition to giving a coordinate-free, intrinsic approach to the theory, we extend the discussion from 5-dimensions to arbitrary dimensions.Our model for space–time–matter is a Ricci flat, semi-Riemannian manifold (E,g¯), where E is a fiber bundle over M (the spacetime) and g¯ is a Kaluza–Klein metric on E. Each space–time–matter manifold (E,g¯) generates spacetimes (M,g˜), one for each embedding of M in E, with stress–energy tensor for M determined by the geometry of E and the nature of the embedding.The use of a fiber bundle E (with fibers isomorphic to the gauge groups) affords a natural way of incorporating the gauge-field potentials into the metric g¯ (perhaps the only global way to do so). The gauge field potentials determine a horizontal bundle orthogonal to the vertical bundle VE of TE and when the spacetime M is embedded horizontally, the gauge fields F vanish when restricted to M. Thus, the fiber bundle approach clarifies how F=0 arises from the geometry rather than from the usual assumptions on the metric in traditional space–time–matter theory.

A NEW APPROACH FOR SPACE-TIME-MATTER THEORY

This is the first paper in a series of three papers on a new approach for space-time-matter (STM) theory. The main purpose of this approach is to replace the Levi-Civita connection on the space-time from the classical Kaluza–Klein theory by what we call the Riemannian horizontal connection on the general Kaluza–Klein space. This is done by a development of a 4D tensor calculus whose geometrical objects live in a 5D space. The 4D tensor calculus and the Riemannian horizontal connection enable us to define in a 5D space some 4D differential operators: horizontal differential, horizontal gradient, horizontal divergence and horizontal Laplacian, which have a great role in the presentation of the STM theory in a covariant form. Finally, we introduce and study the horizontal electromagnetic tensor field, the horizontal Ricci tensor and the horizontal Einstein gravitational tensor field, which replace the well-known tensor fields from the classical Kaluza–Klein theory.

CORRESPONDENCE BETWEEN MODIFIED GRAVITY AND 5D RICCI-FLAT COSMOLOGIES

We study the correspondence between two theoretical frameworks for describing dark energy: f(R) gravity and higher-dimensional space–time–matter (STM) or induced matter theory. We show that the Hubble expansion parameter in f(R) gravity can be associated with a combination of metric functions in STM theory, and consider a specific example whose properties are consistent with late time acceleration.

The geometrical unification of gravity with its source

I give a personal retrospect covering the years during which Mashhoon, myself and others developed a unification of the gravitational field and its source (matter). In this geometrical approach, Einstein’s 4D field equations of general relativity with a source are derived from the 5D Ricci equations for apparent vacuum. The main equations are given, along with comments on how they were arrived at. They describe gravity, electromagnetism and a scalar field. This induced-matter or space–time–matter theory is in agreement with observation and invites further development.

INDUCED PHANTOM AND 5D ATTRACTOR SOLUTION IN SPACETIME–MATTER THEORY

In Spacetime–Matter theory we assume that the 4D induced matter of the 5D Ricci-flat bouncing cosmological solutions contains a perfect fluid as well as an induced scalar field. Then we show that the conventional 4D quintessence and phantom models of dark energy could be recovered from the 5D cosmological solutions. By using the phase-plane analysis to study the stability of evolution of the 5D models, we find that the conventional 4D late-time attractor solution is also recovered. This attractor solution shows that the scale factors of the phantom dominated universes in both the 4D and 5D theories will reach infinity in a finite time and the universes will be ended at a new kind of spacetime singularity at which everything will be annihilated. We also find that the repulsive force of the phantom may provide us with a mechanics to explain the bounce.

INEVITABILITY OF SPACE–TIME SINGULARITIES IN THE CANONICAL METRIC

We discuss the question of whether the existence of singularities is an intrinsic property of 4D space–time. Our hypothesis is that singularities in 4D are induced by the separation of space–time from the other dimensions. We examine this hypothesis in the context of the so-called canonical or warp metrics in 5D. These metrics are popular because they provide a clean separation between the extra dimension and space–time. We show that the space–time section, in these metrics, inevitably becomes singular for some finite (nonzero) value of the extra coordinate. This is true for all canonical metrics that are solutions of the field equations in space–time-matter theory. This is a coordinate singularity in 5D, but appears as a physical one in 4D. At this singular hypersurface, the determinant of the space–time metric becomes zero and the curvature of the space–time blows up to infinity. These results are consistent with our hypothesis.