A COMPLEX FINSLER APPROACH OF GRAVITY

2012 ◽  
Vol 09 (07) ◽  
pp. 1250058 ◽  
Author(s):  
GHEORGHE MUNTEANU ◽  
NICOLETA ALDEA
Keyword(s):  
Gordon Equation ◽  
Finsler Metric ◽  
Energy Relation ◽  
Two Dimensional ◽  
Curvature Invariant ◽  
Plane Wave Solution ◽  
Curvature Invariants ◽  
Complex Finsler Metric ◽  
Klein Gordon ◽  
Special Case

In this paper our aim is mainly to obtain a two-dimensional complex Finsler model of the real gravitation space-time. We prove that, at least in the special case of the weakly gravitational field, this is possible and it leads to some interesting geometrical and physical aspects, such as the study of curvature invariants with respect to complex Berwald frame, intensively studied recently by us for a two-dimensional complex Finsler space. A generalization of the Klein–Gordon equation is proposed and we find solutions which are in concordance to the classical plane wave solution of momentum-energy relation. The last part of the paper is devoted to some applications in which the complex gravitational potential leads to the Bergman metric and to a more general case which leads to a non-purely Hermitian complex Finsler metric, with negative curvature invariant.

Symmetries of generalized Klein-Gordon (including sine-Gordon) equations in three or more dimensions

1987 ◽  
Vol 101 (2) ◽  
pp. 343-348 ◽  
Author(s):  
T. J. Gordon
Keyword(s):  
Conservation Laws ◽  
Gordon Equation ◽  
Nonlinear Partial Differential Equations ◽  
Higher Dimensions ◽  
Higher Order ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Klein Gordon ◽  
Image Position ◽  
Recent Attention

Much recent attention has been devoted to those nonlinear partial differential equations admitting higher-order conservation laws (e.g. [2] and references therein) or equivalently admitting higher-order symmetries. In particular the sine-Gordon equation possesses such symmetries [5, 7] where is the two-dimensional d'Alembertian operator. The question posed and solved here is whether such behaviour is possible in higher dimensions. We therefore consider the ‘Generalized Klein–Gordon’ (GKG) equationin N dimensions where and N ≥ 3.

A method for generating exact solutions of the nonlinear Klein–Gordon equation

1992 ◽  
Vol 70 (6) ◽  
pp. 467-469 ◽  
Author(s):  
A. Grigorov ◽  
N. Martinov ◽  
D. Ouroushev ◽  
Vl. Georgiev
Keyword(s):  
Electromagnetic Field ◽  
Phase Velocity ◽  
Exact Solutions ◽  
Gordon Equation ◽  
External Electromagnetic Field ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Simple Method ◽  
Klein Gordon ◽  
Klein Gordon Equation

A simple method for generating the exact solutions of the nonlinear Klein–Gordon equation is proposed. The solutions obtained depend on two arbitrary functions and are in the form of running waves. An application of one of the solutions for the (2 + 1) – dimensional sine-Gordon equation is proposed. It concerns the selective properties of a two-dimensional semi-infinite Josephson junction with regard to an external electromagnetic field in the form of running waves with a phase velocity equal to the Swihart velocity. A method for measuring the Swihart velocity is presented.

scholarly journals EFFECTS OF A MIXED VECTOR–SCALAR SCREENED COULOMB POTENTIAL FOR SPINLESS PARTICLES

2006 ◽  
Vol 21 (25) ◽  
pp. 5141-5149 ◽  
Author(s):  
ANTONIO S. DE CASTRO
Keyword(s):  
Gordon Equation ◽  
Spinless Particle ◽  
Two Dimensional ◽  
Bounded Solutions ◽  
Screened Coulomb Potentials ◽  
Klein Gordon ◽  
Bona Fide ◽  
Screened Coulomb Potential ◽  
Scalar Potentials ◽  
Coulomb Potentials

The problem of a spinless particle subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and its bounded solutions are found. Some unusual results, including the existence of a bona fide solitary zero-eigenmode solution, are revealed for the Klein–Gordon equation. The cases of pure vector and scalar potentials, already analyzed in previous works, are obtained as particular cases.

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