scholarly journals Quantum Theory of Gravitation

1998 ◽  
Vol 51 (3) ◽  
pp. 459
Author(s):  
H. S. Green
Keyword(s):  
Quantum Theory ◽  
Wave Equations ◽  
Algebraic Method ◽  
Empty Space ◽  
Space Time ◽  
Field Equations ◽  
Gauge Groups ◽  
Gravitational Field Equations ◽  
Non Euclidean Geometry ◽  
Curvature Tensors

It is possible to construct the non-euclidean geometry of space-time from the information carried by neutral particles. Points are identified with the quantal events in which photons or neutrinos are created and annihilated, and represented by the relativistic density matrices of particles immediately after creation or before annihilation. From these, matrices representing subspaces in any number of dimensions are constructed, and the metric and curvature tensors are derived by an elementary algebraic method; these are similar in all respects to those of Riemannian geometry. The algebraic method is extended to obtain solutions of Einstein’s gravitational field equations for empty space, with a cosmological term. General relativity and quantum theory are unified by the quantal embedding of non-euclidean space-time, and the derivation of a generalisation, consistent with Einstein"s equations, of the special relativistic wave equations of particles of any spin within representations of SO(3) ⊗ SO(4; 2). There are some novel results concerning the dependence of the scale of space-time on properties of the particles by means of which it is observed, and the gauge groups associated with gravitation.

scholarly journals Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Debojit Sarma ◽  
Faizuddin Ahmed ◽  
Mahadev Patgiri
Keyword(s):  
Naked Singularity ◽  
Empty Space ◽  
Space Time ◽  
Axially Symmetric ◽  
Field Equations ◽  
Closed Timelike Curves ◽  
Asymptotically Flat ◽  
Type D ◽  
Initial Hypersurface ◽  
Petrov Classification

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The space-time is regular everywhere except on the symmetry axis where it possesses a true curvature singularity. The space-time is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the space-time also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.

LANCZOS–LOVELOCK–CARTAN GRAVITY FROM CLIFFORD-SPACE GEOMETRY

2013 ◽  
Vol 10 (06) ◽  
pp. 1350019 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gravitational Field ◽  
Variational Principle ◽  
Higher Dimensions ◽  
Black Brane ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Gravitational Theories ◽  
Higher Curvature Gravity ◽  
Higher Order Corrections ◽  
Curvature Tensors

A rigorous construction of Clifford-space (C-space) gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the expressions for the connections with torsion in C-spaces. The C-space generalized gravitational field equations are derived from a variational principle based on the extension of the Einstein–Hilbert–Cartan action. We continue by arguing how Lanczos–Lovelock–Cartan (LLC) higher curvature gravity with torsion can be embedded into gravity in C-spaces and suggest how this might also occur for extended gravitational theories based on f(R), f(Rμν), … actions, for polynomial-valued functions. In essence, the LLC curvature tensors appear as Ricci-like traces of certain components of the C-space curvatures. Torsional gravity is related to higher-order corrections of the bosonic string-effective action. In the torsionless case, black-strings and black-brane metric solutions in higher dimensions D > 4 play an important role in finding specific examples of solutions to LL gravity.

scholarly journals NEW GEOMETRIC FORMALISM FOR GRAVITY EQUATION IN EMPTY SPACE

2005 ◽  
Vol 14 (06) ◽  
pp. 1009-1022 ◽  
Author(s):  
XIN-BING HUANG
Keyword(s):  
Differential Equations ◽  
Gauge Field ◽  
Empty Space ◽  
Space Time ◽  
Gravity Theory ◽  
Spin Connection ◽  
Square Root ◽  
Field Equations ◽  
Complex Spin ◽  
Set Up

In this paper, a complex daor field which can be regarded as the square root of space–time metric is proposed to represent gravity. The locally complexified geometry is set up, and the complex spin connection constructs a bridge between gravity and SU(1, 3) gauge field. Daor field equations in empty space are acquired, which are one-order differential equations and do not conflict with Einstein's gravity theory.

GRAVITY IN CURVED PHASE-SPACES, FINSLER GEOMETRY AND TWO-TIMES PHYSICS

2012 ◽  
Vol 27 (12) ◽  
pp. 1250069 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Phase Space ◽  
Tangent Bundle ◽  
Finsler Geometry ◽  
Space Time ◽  
Vacuum Field ◽  
Field Equations ◽  
Problem Of Time ◽  
Gravitational Field Equations ◽  
Cotangent Space ◽  
Kaluza Klein

The generalized (vacuum) field equations corresponding to gravity on curved 2d-dimensional (dim) tangent bundle/phase spaces and associated with the geometry of the (co)tangent bundle TMd-1, 1(T*Md-1, 1) of a d-dim space–time Md-1, 1 are investigated following the strict distinguished d-connection formalism of Lagrange–Finsler and Hamilton–Cartan geometry. It is found that there is no mathematical equivalence with Einstein's vacuum field equations in space–times of 2d dimensions, with two times, after a d+d Kaluza–Klein-like decomposition of the 2d-dim scalar curvature R is performed and involving the introduction of a nonlinear connection [Formula: see text]. The physical applications of the 4-dim phase space metric solutions found in this work, corresponding to the cotangent space of a 2-dim space–time, deserve further investigation. The physics of two times may be relevant in the solution to the problem of time in quantum gravity and in the explanation of dark matter. Finding nontrivial solutions of the generalized gravitational field equations corresponding to the 8-dim cotangent bundle (phase space) of the 4-dim space–time remains a challenging task.

A new approach on electromagnetism with dual number coefficient octonion algebra

2016 ◽  
Vol 13 (09) ◽  
pp. 1630013 ◽  
Author(s):  
Bhupesh Chandra Chanyal ◽  
Sunil Kumar Chanyal ◽  
Özcan Bektaş ◽  
Salim Yüce
Keyword(s):  
Maxwell Equations ◽  
Wave Equations ◽  
Space Time ◽  
Internal Space ◽  
Field Equations ◽  
Octonion Algebra ◽  
New Approach ◽  
Dual Number ◽  
Symmetrical Form ◽  
Unit Formula

Dual number coefficient octonion (DNCO) is one of the kind of octonion, it has 16 components with an additional dual unit [Formula: see text]. Starting with DNCO algebra, we develop the generalized electromagnetic field equations of dyons regarding the DNCOS spaces, which has two octonionic space-times namely the octonionic internal space-time and the octonionic external space-time. Besides, the generalized four-potential components of dyons have been expressed with respect to the dual octonion form. Furthermore, we obtain the symmetrical form of Dirac–Maxwell equations, and the generalized potential wave equations for dyons in terms of the dual octonion. Finally, we conclude that dual octonion formulation is compact and simpler like octonion formulation.

scholarly journals Electrodynamics in Euclidean Space Time Geometries

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 731-742
Author(s):  
Jörn Schliewe
Keyword(s):  
Wave Propagation ◽  
Energy Transport ◽  
Poynting Vector ◽  
Empty Space ◽  
Space Time ◽  
Field Energy ◽  
Field Equations ◽  
Time Coordinate ◽  
Cartesian Space ◽  
Field Energy Density

Abstract In this article it is proven that Maxwell’s field equations are invariant for a real orthogonal Cartesian space time coordinate transformation if polarization and magnetization are assumed to be possible in empty space. Furthermore, it is shown that this approach allows wave propagation with finite field energy transport. To consider the presence of polarization and magnetization an alternative Poynting vector has been defined for which the divergence gives the correct change in field energy density.

scholarly journals A relativistic quantum theory of dyons wave propagation

2017 ◽  
Vol 95 (12) ◽  
pp. 1200-1207 ◽  
Author(s):  
B.C. Chanyal
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Quantum Theory ◽  
Quantum Electrodynamics ◽  
Wave Equations ◽  
Relativistic Quantum ◽  
Relativistic Wave Equation ◽  
Field Equations ◽  
Continuity Equations ◽  
Quantum Wave

Beginning with the quaternionic generalization of the quantum wave equation, we construct a simple model of relativistic quantum electrodynamics for massive dyons. A new quaternionic form of unified relativistic wave equation consisting of vector and scalar functions is obtained, and also satisfy the quaternionic momentum eigenvalue equation. Keeping in mind the importance of quantum field theory, we investigate the relativistic quantum structure of electromagnetic wave propagation of dyons. The present quantum theory of electromagnetism leads to generalized Lorentz gauge conditions for the electric and magnetic charge of dyons. We also demonstrate the universal quantum wave equations for two four-potentials as well as two four-currents of dyons. The generalized continuity equations for massive dyons in case of quantum fields are expressed. Furthermore, we concluded that the quantum generalization of electromagnetic field equations of dyons can be related to analogous London field equations (i.e., current to electromagnetic fields in and around a superconductor).

ENTROPY DENSITY OF SPACE–TIME AND GRAVITY: A CONCEPTUAL SYNTHESIS

2009 ◽  
Vol 18 (14) ◽  
pp. 2189-2193 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Quantum Theory ◽  
Quantum Gravity ◽  
Invariant Theory ◽  
Entropy Density ◽  
Space Time ◽  
General Covariance ◽  
Principle Of Equivalence ◽  
Field Equations ◽  
Accelerated Observers ◽  
Thermodynamic Interpretation

I show that combining the principle of equivalence and the principle of general covariance with the known properties of local Rindler horizons, perceived by accelerated observers, leads to the following inescapable conclusion: The field equations describing gravity in any diffeomorphism-invariant theory must have a thermodynamic interpretation. This synthesis of quantum theory, thermodynamics and gravity shows that the gravitational dynamics can be interpreted completely in terms of entropy balance between matter and space–time. This idea has far-reaching implications for the microstructure of space–time and quantum gravity.

A SOLUTION OF THE EINSTEIN FIELD EQUATIONS

1960 ◽  
Vol 38 (12) ◽  
pp. 1661-1664
Author(s):  
Peter Rastall
Keyword(s):  
Empty Space ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Gravitational Field Equations ◽  
Axis Of Symmetry ◽  
Time Dependent Solution ◽  
Empty Universe ◽  
Number Of Particles

An exact, cylindrically symmetric, time-dependent solution of the Einstein gravitational field equations for empty space is derived. A particular case of the solution has singularities only on the axis of symmetry and may represent a number of particles in an otherwise empty universe.

scholarly journals GENERATING FUNCTIONAL FOR THE GRAVITATIONAL FIELD: IMPLEMENTATION OF AN EVOLUTIONARY QUANTUM DYNAMICS

2005 ◽  
Vol 14 (10) ◽  
pp. 1739-1760
Author(s):  
ERIKA CERASTI ◽  
GIOVANNI MONTANI
Keyword(s):  
Quantum Theory ◽  
Gravitational Field ◽  
Quantum Dynamics ◽  
Hamiltonian Formalism ◽  
Field Equations ◽  
Lagrangian Multipliers ◽  
Generating Functional ◽  
Mean Values ◽  
Classical Counterpart ◽  
Gravitational Field Equations

We provide a generating functional for the gravitational field that is associated with the relaxation of the primary constraints by extending to the quantum sector. This requirement of the theory relies on the assumption that a suitable time variable exists, when taking the T-products of the dynamical variables. More precisely, we start from the gravitational field equations written in the Hamiltonian formalism and expressed via Misner-like variables; hence we construct the equation to which the T-products of the dynamical variables obey and transform this paradigm in terms of the generating functional, as taken on the theory phase-space. We show how the relaxation of the primary constraints (which corresponds to the breakdown of the invariance of the quantum theory under the four-diffeomorphisms) is summarized by a free functional taken on the Lagrangian multipliers, accounting for such constraints in the classical theory. The issue of our analysis is equivalent to a Gupta–Bleuler approach on the quantum implementation of all the gravitational constraints; in fact, in the limit of small ℏ, the quantum dynamics is described by a Schrödinger equation as soon as the mean values of the momenta, associated to the lapse function and the shift vector, are not vanishing. Finally we show how, in the classical limit, the evolutionary quantum gravity reduces to General Relativity in the presence of an Eckart fluid, which corresponds to the classical counterpart of the physical clock, introduced in the quantum theory.

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