scholarly journals Differential form approach for stationary axisymmetric Maxwell fields in general relativity

1994 ◽  
Vol 11 (6) ◽  
pp. 1489-1504 ◽  
Author(s):  
L Fernández-Jambrina ◽  
F J Chinea
Keyword(s):  
General Relativity ◽  
Differential Form ◽  
Maxwell Fields ◽  
Form Approach

Least Action and Classical Fields

2021 ◽  
pp. 286-325
Author(s):  
Moataz H. Emam
Keyword(s):  
General Relativity ◽  
Momentum Tensor ◽  
Point Particle ◽  
Kerr Metric ◽  
Field Equations ◽  
Tensor Fields ◽  
Particle Mechanics ◽  
Least Action ◽  
Principle Of Least Action ◽  
Maxwell Fields

We present the principle of least action and see how it is used in non-relativistic point particle mechanics, relativistic point particle mechanics, general relativity, derivation of field equations for scalar, vector and tensor fields as well as the energy momentum tensor. Towards the end we present examples of solutions of Einstein-Maxwell fields: The Reissner-Nordstrom metric, Kerr metric, and Kerr- Newman metric.

scholarly journals Calculus of variations: A differential form approach

2019 ◽  
Vol 12 (1) ◽  
pp. 57-84 ◽  
Author(s):  
Swarnendu Sil
Keyword(s):  
Continuous Function ◽  
Calculus Of Variations ◽  
Differential Form ◽  
Lower Semicontinuity ◽  
Weak Continuity ◽  
Minimization Problems ◽  
Weak Lower Semicontinuity ◽  
Form Approach

AbstractWe study integrals of the form {\int_{\Omega}f(d\omega_{1},\dots,d\omega_{m})}, where {m\geq 1} is a given integer, {1\leq k_{i}\leq n} are integers, {\omega_{i}} is a {(k_{i}-1)}-form for all {1\leq i\leq m} and {f:\prod_{i=1}^{m}\Lambda^{k_{i}}(\mathbb{R}^{n})\rightarrow\mathbb{R}} is a continuous function. We introduce the appropriate notions of convexity, namely vectorial ext. one convexity, vectorial ext. quasiconvexity and vectorial ext. polyconvexity. We prove weak lower semicontinuity theorems and weak continuity theorems and conclude with applications to minimization problems. These results generalize the corresponding results in both classical vectorial calculus of variations and the calculus of variations for a single differential form.

Differential Forms

2021 ◽  
pp. 326-357
Author(s):  
Moataz H. Emam
Keyword(s):  
General Relativity ◽  
Differential Forms ◽  
Modern Theory ◽  
Maxwell Fields ◽  
Classical Fields

In this chapter we present the modern theory of differential forms and see how it applies to the classical fields studied in the previous chapter. We apply the theory to Maxwell fields as well as to Cartan’s formulation of general relativity. A discussion of the generalized Stokes theorem is given.

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