Born–Infeld solution for a point charge in D dimensions

1993 ◽  
Vol 71 (9-10) ◽  
pp. 484-487
Author(s):  
C. Wolf
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Charged Particle ◽  
Point Charge ◽  
Total Mass ◽  
Space Time

By considering the generalization to D space-time dimensions of the Born–Infeld Lagrangian we evaluate the electromagnetic field and gravitational field of a point charge and derive an expression for the total mass of a point charged particle in this theory.

THE GRAVITOKINETIC FIELD AND THE ORBIT OF MERCURY

1966 ◽  
Vol 44 (5) ◽  
pp. 1147-1156 ◽  
Author(s):  
J. C. W. Scott
Keyword(s):  
Field Theory ◽  
Electromagnetic Field ◽  
Gravitational Field ◽  
Electromagnetic Force ◽  
Total Mass ◽  
Gravitational Force ◽  
Space Time ◽  
Red Shift ◽  
Null Results ◽  
Magnetic Components

A new Lorentz-invariant gravitational field theory is introduced according to which space–time is always flat. The gravitational field is of Maxwellian form with potential and kinetic components analogous to the electric and magnetic components of the electromagnetic field. New mathematical entities named scaled tensors are developed. While the electromagnetic force is represented by an unsealed tensor, the gravitational force is properly described by a scaled tensor. The precession of the orbit of the planet Mercury establishes the scale of the gravitational force as −5. Since the force on a body is found to be proportional to its total mass, the null results of Eötvös and Dicke are confirmed. However, the theory requires that the force depend on velocity so that new very small effects analogous to electromagnetic phenomena are predicted. In a following paper, "Photons in the Gravitational Field", the gravitational red shift and the gravitational deflection of a light ray are deduced correctly.

scholarly journals On the potential of electromagnetic phenomena in a gravitational field

1928 ◽  
Vol 120 (784) ◽  
pp. 1-13
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Electromagnetic Theory ◽  
Space Time ◽  
Electromagnetic Potential ◽  
Vector Potentials ◽  
Type Form ◽  
Action At A Distance ◽  
Galilean Space

In classical electromagnetic theory, the electromagnetic field due to any number of electrons moving in any manner is determined by a theorem which expresses the scalar and vector potentials of the field in terms of the positions and velocities of the electrons. The theorem may be stated thus: Denoting by t ¯ the instant at which radiation was emitted from an electron e so as to reach a point P ( x, y, z ), at the instant t , by ( x´ ¯ , y´ ¯ , z´ ¯ ) the co-ordinates of the electron at the instant t ¯ , by r ¯ the distance between the points ( x´ ¯ , y´ ¯ , z´ ¯ ) and ( x, y, z ) and by ( v x , v y , v z ) the components of velocity of the electron at the instant t ¯ , then the four-vector of the electromagnetic potential at P, due to the electron e , is ( Φ 0 , Φ 1 , Φ 2 , Φ 3 ) = ( e / s , - ev x / s , ev y / s , ev z / s ), (1) where s = r ¯ + {( x´ ¯ - x ) v x + ( y´ ¯ - y ) v y + ( z´ ¯ - z ) v z }/ c . The object of the present paper is to study the extension of this theorem to electromagnetic field which contain gravitating masses, so that the metric of space-time is no longer Galilean. It is obvious at the outset that there will be difficulty in making such an extension, because the quantities occurring in formula (1) cannot readily be generalised to non-Galilean space-time; the quantities r ¯ and s , in fact, belong essentially to action-at-a-distance theories, and therefore if a formula exists which expresses the electromagnetic potential in a gravitational field in terms of the electric charges and their motions, it must be altogether different in type form the formula (1) above.

scholarly journals Space-Time Geometry of Electromagnetic Field in the System of Photon

2013 ◽  
Vol 14 ◽  
pp. 13-16
Author(s):  
Mukul Chandra Das ◽  
Rampada Misra
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Gravitational Field ◽  
Space Time

In the concept of general relativity gravity is the space-time geometry. Again, a relation between electromagnetic field and gravitational field is expected. In this paper, space-time geometry of electromagnetic field in the system of photon has been introduced to unify electromagnetic field and gravitational field in flat and curvature space-time.

Self-conjugate gravitational fields. I

1963 ◽  
Vol 275 (1361) ◽  
pp. 245-256 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Flat Space ◽  
Space Time ◽  
Second Order ◽  
Necessary Condition ◽  
Tensor Form ◽  
Gravitational Fields ◽  
Null Electromagnetic Field ◽  
Scalar Invariants

By splitting the curvature tensor R hijk into three 3-tensors of the second rank in a normal co-ordinate system, self-conjugate empty gravitational fields are defined in a manner analogous to that of the electromagnetic field. This formalism leads to three different types of self-conjugate gravitational fields, herein termed as types A, B and C . The condition that the gravitational field be self-conjugate of type A is expressed in a tensor form. It is shown that in such a field R hijk is propagated with the fundamental velocity and all the fourteen scalar invariants of the second order vanish. The structure of R hijk defines a null vector which can be identified as the vector defining the propagation of gravitational waves. It is found that a necessary condition for an empty gravitational field to be continued with a flat space-time across a null 3-space is that the field be self-conjugate of type A. The concept of the self-conjugate gravitational field is extended to the case when R ij # 0 but the scalar curvature R is zero. The condition in this case is also expressed in a tensor form. The necessary conditions that the space-time of an electromagnetic field be continued with an empty gravitational field or a flat space-time across a 3-space have been obtained. It is shown that for a null electromagnetic field whose gravitational field is self-conjugate of type A , all the fourteen scalar invariants of the second order vanish.

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

The spin-zero Duffin-Kemmer-Petiau equation in a cosmic-string space-time with the Cornell interaction

2016 ◽  
Vol 31 (36) ◽  
pp. 1650191 ◽  
Author(s):  
M. de Montigny ◽  
M. Hosseinpour ◽  
H. Hassanabadi
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Cosmic String ◽  
Topological Defects ◽  
Space Time ◽  
Dkp Equation

In this paper, we study the covariant Duffin-Kemmer-Petiau (DKP) equation in the cosmic-string space-time and consider the interaction of a DKP field with the gravitational field produced by topological defects in order to examine the influence of topology on this system. We solve the spin-zero DKP oscillator in the presence of the Cornell interaction with a rotating coordinate system in an exact analytical manner for nodeless and one-node states by proposing a proper ansatz solution.

Mechanics of a charged particle on the Kaluza–Klein background

1995 ◽  
Vol 73 (9-10) ◽  
pp. 602-607 ◽  
Author(s):  
S. R. Vatsya
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Integral Method ◽  
Gordon Equation ◽  
Type Equation ◽  
Fifth Dimension ◽  
Klein Gordon ◽  
Path Integral Method ◽  
Klein Gordon Equation ◽  
Kaluza Klein

The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.

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