Null electromagnetic fields in a general relativity

1970 ◽  
Vol 3 (5) ◽  
pp. 501-504 ◽  
Author(s):  
A Banerjee
Keyword(s):  
General Relativity ◽  
Electromagnetic Fields

On Almost Contingent Manifolds of Second Class with Applications in Relativity

1978 ◽  
Vol 21 (3) ◽  
pp. 289-295 ◽  
Author(s):  
K. L. Duggal
Keyword(s):  
General Relativity ◽  
Electromagnetic Fields ◽  
Vector Fields ◽  
Killing Vector ◽  
Positive Definite ◽  
Geometric Proof ◽  
Sasakian Manifolds ◽  
Killing Vector Fields ◽  
Degenerate Metric ◽  
Frame Work

D. E. Blair [1] has introduced the notion of K-manifolds as an analogue of the even dimensional Kähler manifolds and of the odd dimensional quasi-Sasakian manifolds. These manifolds have been studied with respect to a positive definite metric. In this paper, we study a more general case of if-manifolds carrying an arbitrary non-degenerate metric, in particular, a metric of Lorentz signature. This theory is then applied within the frame-work of general relativity. Using the Ruse-Synge classification [8, 9] of non-null electromagnetic fields with source, we develop a geometric proof for the existence of either two space like or one space like and one time like Killing vector fields on the space-time manifold.

Some wave solutions in general relativity

1974 ◽  
Vol 75 (2) ◽  
pp. 261-267
Author(s):  
L. K. Patel
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Electromagnetic Fields ◽  
General Scheme ◽  
Wave Solutions ◽  
Particular Solution

AbstractA general scheme for the derivation of wave solutions in general relativity is developed. Some solutions describing the flow of gravitational waves are discussed. Singular electromagnetic fields corresponding to one particular solution are also discussed.

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.

GEOMETRICAL PROPERTIES OF ELECTROMAGNETIC TIDAL FORCES

2010 ◽  
Vol 25 (29) ◽  
pp. 5383-5398
Author(s):  
ÉRICO GOULART ◽  
FELIPE TOVAR FALCIANO
Keyword(s):  
General Relativity ◽  
Electromagnetic Fields ◽  
Local Field ◽  
Degrees Of Freedom ◽  
Charged Particles ◽  
Tidal Effects ◽  
Geometrical Properties ◽  
Tidal Forces ◽  
Field Lines ◽  
Internal Degrees Of Freedom

In general, elementary particles as well as extensive bodies have internal degrees of freedom that naturally turn their trajectories into accelerated curves. Hence, we propose to describe the kinematical properties of nongeodesic congruences and study how tidal forces are modified. Once the general scenario is well established, we analyze in details tidal effects due to electromagnetic fields, i.e. the relative acceleration between test charged particles. An algebraic analysis of these fields is developed together with a geometrical interpretation in terms of local field lines. In this framework, we compare general relativity and electrodynamics in terms of operationally equivalent objects.

scholarly journals GRAVITATION, ELECTROMAGNETISM AND THE COSMOLOGICAL CONSTANT IN PURELY AFFINE GRAVITY

2009 ◽  
Vol 18 (05) ◽  
pp. 809-829 ◽  
Author(s):  
NIKODEM J. POPŁAWSKI
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Electromagnetic Fields ◽  
Ricci Tensor ◽  
Einstein Equations ◽  
Metric Tensor ◽  
Affine Metric ◽  
Affine Gravity

The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris–Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein–Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric–affine/metric formulation. We also show that such a construction is valid only for weak electromagnetic fields. Therefore the purely affine formulation that combines gravitation, electromagnetism and the cosmological constant cannot be a simple sum of terms corresponding to separate fields. Consequently, this formulation of electromagnetism seems to be unphysical, unlike the purely metric and metric–affine pictures, unless the electromagnetic field couples to the cosmological constant.

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