Teleparallel Lagrange geometry and a unified field theory

Abstract

Abstract. In this paper, we construct a field theory unifying gravity and electromagnetism in the context of Extended Absolute Parallelism (EAP-) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and the mathematical simplicity of Absolute Parallelism (AP-) geometry. The constructed field theory is a generalization of the Generalized Field Theory (GFT) formulated by Mikhail and Wanas. The theory obtained is purely geometric. The horizontal (resp. vertical) field equations are derived by applying the Euler-Lagrange equations to an appropriate horizontal (resp. vertical) scalar Lagrangian. The symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Einstein's field equations in which the horizontal (resp. vertical) energy-momentum tensor is purely geometric. The skew-symmetric part of the resulting horizontal (resp. vertical) field equations gives rise to a generalized form of Maxwell equations in which the electromagnetic field is purely geometric. Some interesting special cases, which reveal the role of the nonlinear connection in the obtained field equations, are examined. Finally, the condition under which our constructed field equations reduce to the GFT is explicitly established.

Conserved charges of Schwarzschild-NUT-AdS space–time using the method of regularization through relocalization

“…We calculate the necessary components needed for Eq. (15). The non-vanishing components of N ab have the form 5…”

“…The Poincaré gauge theory (PGT) is a gauge formulation of gravity which represents, at least at the classical level, a viable alternative to GR [15][16][17][18][19][20][21]. The investigation of the canonical structure of PGT has led to a significant improvement of our understanding of its gauge and physical properties [22].…”

Connections in sub-Riemannian geometry of parallelizable distributions

“…Sub-Riemannian Geometry [1,4,10,15,16] has many applications such as diffusion, mechanics, gauge theories and control theory [7,13]. Absolute parallelism geometry or the geometry of parallelizable manifolds [3,17,20,21] is frequently used for applications in physics, especially in the geometrization of physical theories such general relativity and gravitation [6,12,14,18,19].…”

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

“…It has been shown that many other scalars can be defined in AP-geometry and its different versions. These scalars have been used to construct several field theories with GR limits [13,28,30,34,35,36].…”