Maxwell’s theory on a post-Riemannian spacetime and the equivalence principle
نویسندگان
چکیده
The form of Maxwell’s theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or nonmetricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or nonmetricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (comprising torsion and nonmetricity). All this is compared to the recent results of Vandyck.
منابع مشابه
Simultaneous emergence of curved spacetime and quantum mechanics
It is shown in this paper that the geometrically structure-less spacetime manifold is converted instantaneously to a curved one, the Riemannian or may be a Finslerian spacetime with an associated Riemannian spacetime, on the appearance of quantum Weyl spinors dependent only on time in that background flat manifold and having the symplectic property in the abstract space of spinors. The scenario...
متن کاملOn the Equivalence Principle and a Unified Description of Gravitation and Electromagnetism
We first investigate the form the general relativity theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence principle for the electromagnetic field. We argue that to each particle with a different electric charge-to-mass ratio in a gravitational and electromagnetic...
متن کاملDark Energy and Emergent Spacetime
A natural geometric framework of noncommutative spacetime is symplectic geometry rather than Riemannian geometry. The Darboux theorem in symplectic geometry then admits a novel form of the equivalence principle such that the electromagnetism in noncommutative spacetime can be regarded as a theory of gravity. Remarkably the emergent gravity reveals a noble picture about the origin of spacetime, ...
متن کاملPost-Riemannian Merger of Weyl and/or Yang-Mills Interactions with Gravity
We show that a spacetime with torsion and non-metricity, obtained as a deformation of a Riemannian spacetime, accommodates an internal symmetry structure of the YangMills prototype in such a way that the internal symmetry becomes an integral part of the spacetime itself. In particular, the spacetime structural identities, which become “contaminated” by internal degrees of freedom, remain invari...
متن کاملun 2 00 4 On geodesic equivalence of Riemannian metrics and sub - Riemannian metrics on distributions of corank 1 Igor
The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new...
متن کامل