In Kaluza derived theories the electromagnetic potential is interpreted as a part of the metric in a higher dimensional theory of gravity. Here we present a more Yang-Mills like unification of classical electromagnetism and gravity within five dimensions, where the electromagnetic potential is related to the connecion and the field strength to the curvature. In addition some aspects of a quantum theory can be described in the context of the Gauss-Bonnet-Chern Theorem. This approach offers new coupling mechanisms between gravity and electromagnetism.
We apply Kaluza's procedure to Eddington-inspired Born-Infeld action in gravity in five dimensions. The resulting action contains, in addition to the usual four-dimensional actions for gravity and electromagnetism, nonlinear couplings between the electromagnetic field strength and curvature. Considering the spherically symmetric solution as an example we find the lowest order corrections for the Reissner-Nordström metric and the electromagnetic field.
We study Kaluza-Klein reduction in Newton-Cartan gravity. In particular we show that dimensional reduction and the nonrelativistic limit commute. The resulting theory contains Galilean electromagnetism and a nonrelativistic scalar. It provides the first example of back-reacted couplings of scalar and vector matter to Newton-Cartan gravity. This back-reaction is interesting as it sources the spatial Ricci curvature, providing an example where nonrelativistic gravity is more than just a Newtonian potential.
In this paper, Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ratio has a physical meaning of the ratio between the movement along the direction of the 5th axis and the movement in the 4D space-time. In order to have a 5D matter which is consistent with the construction of the 5D manifold, a notion of particle-thread is suggested. Examinations on the compatibility of reference frames reveal a covariance …
We propose in this paper a new approach to the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering a natural geometric definition of a matter fluid and abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing new physics, w…
It is shown that the pre-metric approach to Maxwell's equations provides an alternative to the traditional Einstein-Maxwell unification program, namely, that electromagnetism and gravitation are unified in a different way that makes the gravitational field a consequence of the electromagnetic constitute properties of spacetime, by way of the dispersion law for the propagation of electromagnetic waves.
We consider the coupling of the electromagnetic field to a non-local gravity theory comprising of the Einstein-Hilbert action in addition to a non-local $R\, {\Box}^{-2} R$ term associated with a mass scale $m$. We demonstrate that in the case of the minimally coupled electromagnetic field, real corrections about the Reissner-Nordström background only exist between the inner Cauchy horizon and the event horizon of the black hole. This motivates us to consider the modified coupling of electromagnetism to this theory via the Kaluza ansatz. The Kaluza reduction introduces non-local terms involvin…
Kaluza-Klein theory is a popular alternative theory of gravity, with both non-rotating and rotating black hole solutions known. This allows for the possibility that the theory could be observationally tested. We present a model which calculates the reflection spectrum of a black hole accretion disk system, where the black hole is described by a rotating solution of the Kaluza-Klein theory. We also use this model to analyze X-ray data from the stella-mass black hole in GRS 1915+105 and provide constraints on the free parameters of the Kaluza-Klein black holes.
We study the case in which the five dimensional theory is the transformed Weyl$-$Yang$-$Kaluza$-$Klein gravity. The dimensionally reduced equations of motion are derived by considering an alternative form of the main equation of the theory in the coordinate basis. The conformal transformation rules are applied to the invariants. We also discuss the possible specific cases and the new Lorentz force density term, in detail.
During the last century, two independent theories using the concept of dimensional reduction have been developed independently. The first, known as Föppl-von Kàrmàn theory, uses Riemannian geometry and continuum mechanics to study the shaping of thin elastic structures which could become as complex as crumpled paper. The second one, known as Kaluza-Klein theory, uses Minkowskian geometry and general relativity to unify fundamental interactions and gravity under the same formalism. Here we draw a parallel between these two theories in an attempt to use concepts from elasticity theory of plates …
Correlated parity violation in gravity and electromagnetism from five-dimensional spacetime
School of Intelligent Engineering, Shaoguan University（韶关学院智能工程学院）；Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）
To perform realistic tests of theories of gravity, we need to be able to look beyond general relativity and evaluate the consistency of alternative theories with observational data from, especially, gravitational wave detections using, for example, an agnostic Bayesian approach. In this paper we further examine properties of one class of such viable, alternative theories, based on metrics arising from ungauged supergravity. In particular, we examine the massless, neutral, minimally coupled scalar wave equation in a general stationary, axisymmetric background metric such as that of a charged ro…
The observed red shift $z$ might be composed by the expansion red shift $z_{\rm C}$ and an additional frequency shift $z_{\rm S}$, towards the red or the blue, by considering Extended Theories of Electromagnetism (ETE). Indeed, massive photon theories - the photon has a real mass as in the de Broglie-Proca theory or an effective mass as in the Standard-Model Extension (SME), based on Lorentz-Poincaré Symmetry Violation (LSV) - or Non-Linear Electro-Magnetism (NLEM) theories may induce a cosmological expansion independent frequency shift in presence of background (inter-) galactic electromagnet…
