A Field Theory with Curvature and Anticurvature

Abstract

The present work is an attempt to construct a unified field theory in a space with curvature and anticurvature, the PAP-space. The theory is derived from an action principle and a Lagrangian density using a symmetric linear parameterized connection. Three different methods are used to explore physical contents of the theory obtained. Poisson’s equations for both material and charge distributions are obtained, as special cases, from the field equations of the theory. The theory is a pure geometric one in the sense that material distribution, charge distribution, gravitational and electromagnetic potentials, and other physical quantities are defined in terms of pure geometric objects of the structure used. In the case of pure gravity in free space, the spherical symmetric solution of the field equations gives the Schwarzschild exterior field. The weak equivalence principle is respected only in the case of pure gravity in free space; otherwise it is violated.

Motion of Charged Spinning Particles in a Unified Field

“…Other authors [9] have used this relation to interpret the huge magnetic field producing gamma ray bursts. Now, in the present work, we are dealing with a pure geometric theory unifying gravity and electromagnetism [10]. So, we expect both types (as will appear in this discussion, two types of electromagnetism appear in the Universe.)…”

“…As a usual procedure, we solve the field equations before solving the equations of motion as usually done in GR. In the present work, the field equations [10] are in general sixteen in number while the equations of motion (Equation (43)) are four. After solving the field equation, sixteen field variables become known functions of the coordinate.…”

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

“…The curves (paths) of the geometry have been derived [22] and used to describe the motion of spinning particles [32,33]. Geometric objects have been used to represent physical quantities via the constructed field theories [30,35].…”

“…The identity (5.2) is thus an identity of PAP-geometry, independent of any such field theory. The tensor * T µν is usually used as a geometric representation of a material-energy distribution in any field theory constructed in PAPgeometry [30,35].…”

“…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].…”