EQUATIONS OF MOTION FOR SPACE-TIME-MATTER THEORY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350018
Author(s):  
AUREL BEJANCU
Keyword(s):  
Equations Of Motion ◽  
Space Time ◽  
Relativity Theory ◽  
Covariant Form ◽  
General Relativity Theory ◽  
Full Generality ◽  
New Approach ◽  
Base Manifold ◽  
Matter Theory ◽  
Kaluza Klein

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).

scholarly journals On Higher Dimensional Kaluza-Klein Theories

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Aurel Bejancu
Keyword(s):  
General Relativity ◽  
Lorentz Force ◽  
Equations Of Motion ◽  
New Method ◽  
Covariant Form ◽  
Tensor Fields ◽  
New Approach ◽  
Higher Dimensional ◽  
General Gauge ◽  
Kaluza Klein

We present a new method for the study of general higher dimensional Kaluza-Klein theories. Our new approach is based on the Riemannian adapted connection and on a theory of adapted tensor fields in the ambient space. We obtain, in a covariant form, the fully general 4D equations of motion in a (4 +n)D general gauge Kaluza-Klein space. This enables us to classify the geodesics of the (4 +n)D space and to show that the induced motions in the 4D space bring more information than motions from both the 4D general relativity and the 4D Lorentz force equations. Finally, we note that all the previous studies on higher dimensional Kaluza-Klein theories are particular cases of the general case considered in the present paper.

Modified field equations from a complexified nonlocal metric

2019 ◽  
Vol 97 (8) ◽  
pp. 816-827
Author(s):  
Rami Ahmad El-Nabulsi
Keyword(s):  
General Relativity ◽  
Covariant Derivative ◽  
Equations Of Motion ◽  
Space Time ◽  
Relativity Theory ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
General Relativity Theory ◽  
Higher Derivative ◽  
Tangent Vectors

We argue that it is possible to obtain higher-derivative Einstein’s field equations by means of an extended complexified backward–forward nonlocal extension of the space–time metric, which depends on space–time vectors. Our approach generalizes the notion of the covariant derivative along tangent vectors of a given manifold, and accordingly many of the differential geometrical operators and symbols used in general relativity. Equations of motion are derived and a nonlocal complexified general relativity theory is formulated. A number of illustrations are proposed and discussed accordingly.

On the differential topology of space-time

1971 ◽  
Vol 69 (2) ◽  
pp. 295-296 ◽  
Author(s):  
J. Wolfgang Smith
Keyword(s):  
General Relativity ◽  
Life History ◽  
Space Time ◽  
Average Density ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Differential Topology ◽  
Cosmology Theory ◽  
History Of

It has often been assumed in cosmology theory(1) that there exists an average density of matter in space which is everywhere greater than zero. Under this assumption the space-time M will be foliated by curves each of which represents the life history of a particle. In keeping with the postulates of general relativity theory we shall refer to these curves as geodesics. Letting X denote the space of particles one obtains a projection f: M → X which assigns to every P ∈ M the particle found at P. Conversely, given the projection f:M → X, one can recover the geodesics: they are precisely the fibres f−1(x), x∈X.

A NEW APPROACH FOR SPACE-TIME-MATTER THEORY

2013 ◽  
Vol 10 (04) ◽  
pp. 1350004 ◽  
Author(s):  
AUREL BEJANCU
Keyword(s):  
Tensor Field ◽  
Differential Operators ◽  
Space Time ◽  
Horizontal Gradient ◽  
Tensor Fields ◽  
Tensor Calculus ◽  
New Approach ◽  
Horizontal Connection ◽  
Klein Theory ◽  
Kaluza Klein

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.

scholarly journals Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Wave Equations ◽  
Gordon Equation ◽  
Space Time ◽  
Wave Functions ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Gauge Fixing ◽  
Klein Gordon ◽  
Klein Gordon Equation

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

scholarly journals Possible Unification of Quantum Mechanics and General Relativity Theory Based on the Three-Dimensional Quantized Spaces

2018 ◽  
Author(s):  
Jae-Kwang Hwang
Keyword(s):  
General Relativity ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Energy Transition ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Dimensional Space Time

Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (Dt=tq). The energy is newly defined as the 4-dimensional space-time volume of E = cDtDV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4-dimensional space-time volume and the 4-dimensional space-time distance, respectively.

scholarly journals Einstein’s Notational Equation of Electro-Magnetic Field Equation in Rindler spacetime

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Field Equation ◽  
Electromagnetic Fields ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Electro Magnetic Field ◽  
Rindler Space ◽  
Electro Magnetic

We find Einstein’s notational equation of the electro-magnetic field equation and the electromagneticfield in Rindler space-time. Because, electromagnetic fields of the accelerated frame include in general relativity theory.

Massive and massless scalar field models for Kaluza–Klein universe in f(R, T) gravity

2019 ◽  
Vol 34 (11) ◽  
pp. 1950066 ◽  
Author(s):  
Can Aktaş
Keyword(s):  
Scalar Field ◽  
Cosmological Term ◽  
Relativity Theory ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
General Relativity Theory ◽  
Text Model ◽  
The Universe ◽  
Kaluza Klein

In this research, we have investigated the behavior of massive and massless scalar field (SF) models (normal and phantom) for Kaluza–Klein universe in [Formula: see text] gravity with cosmological term ([Formula: see text]). To obtain field equations, we have used [Formula: see text] model given by Harko et al. [Phys. Rev. D 84, 024020 (2011)] and anisotropy feature of the universe. Finally, we have discussed our results in [Formula: see text] and General Relativity Theory (GRT) with various graphics.

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