More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically different quantities (meter, second, coulomb etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudo-Riemannian one, a multiple fibered semi-Riemannian geometry is the most appropriate one for the treatment of more then three different physical quantities as unified geometrical field theory.
Semi-Euclidean geometry $^{3}R_5^4$ with 1-dimensional fiber $x^5$ and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry $^{3}V_5^4$ with the general relativity pseudo-Riemannian space-time $^{3}V^4,$ and 1-dimensional fiber $x^5,$ responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the 5-th coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise.
PACS: 04.50.Cd, 02.40.-k, 11.10.Kk
Comments on the Unification of Electromagnetism and Gravitation through "Generalized Einstein manifolds"
H. Akbar-Zadeh最近提出了（J Geom Phys 17（1995）342）一种新的关于广义Einstein流形的Einstein-Maxwell系统的几何表述。我们表明，相反的索赔，麦克斯韦方程组没有推导出在这个配方，假设的方程可以被确定为无源麦克斯韦方程组在建议的几何设置。一个真正的推导无源麦克斯韦方程组在同一框架内。我们得出的结论是，建议的统一计划只能适用于无源的情况。
From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor equations of motion, the gravitational continuity equation, the conservation of the energy, the energy-momentum tensor, the field tensor, and the constraints concerning these fields. The Lagrangian formulation is also exhibited as an unified and simple formulation that will be useful for future investigation.
Following earlier works of Dereli and collaborators, we study a three dimensional toy model where we extend the topologically massive gravity with electrodynamics by the most general $RF^2$-type non-minimal coupling terms. Here $R$ denotes the possible curvature terms and $F$ denotes the electromagnetic 2-form. We derive the variational field equations and look for exact solutions on constant negative curvature space-times with a constant, self-dual electromagnetic field. The notion of self-dual electromagnetic fields in three dimensions is introduced by Dereli and collaborators in the study o…
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 superimposed gravitational and electromagnetic fields there corresponds a spacetime manifold whose metric tensor $g_{μν}$ describes the dynamical actions of gravitation and electromagnetism. The electric field outside a charged sphere ass…
In this work, we focus on the theory of Gravito-Electromagnetism (GEM) -- the theory that describes the dynamics of the gravitational field in terms of quantities met in Electromagnetism -- and we propose two novel forms of metric perturbations. The first one is a generalisation of the traditional GEM ansatz, and succeeds in reproducing the whole set of Maxwell's equations even for a dynamical vector potential A. The second form, the so-called alternative ansatz, goes beyond that leading to an expression for the Lorentz force that matches the one of Electromagnetism and is free of additional t…
The flux of angular momentum in electromagnetism cannot be expressed entirely in terms of the field's radiative degrees of freedom. Its expression also involves Coulombic pieces of the field, in the form of a charge aspect $q(θ,ϕ)$, a function of polar angles whose integral gives the total charge of the system. Guided by the strong analogy between radiative processes in electromagnetism and gravitation, we ask whether the flux of angular momentum in general relativity might also involve Coulombic pieces of the gravitational field. Further, we ask whether such terms might have been missed in th…
In electromagnetism, the concept of Poynting vector as measured by an observer is well known. A mathematical analogue in general relativity is the super-Poynting vector of the Weyl tensor. Observers for which the (super-)Poynting vector vanishes are called principal. When, at a given point, the electromagnetic field is non-null, or the gravitational field is of Weyl-Petrov type I or D, principal observers instantaneously passing through that point always exist. We survey characterizations of such observers and study their relation to arbitrary observers. In the non-null electromagnetic case it…
In this paper we extend the quasitopological electromagnetism, recently introduced by H.-S. Liu et al. [arXiv:1907.10876], to arbitrary dimensions by introducing a fundamental $p$-form field. This allows us to construct new dyonic black hole solutions in odd dimensions, as well as regular $D$-dimensional black holes and solitons. The three-dimensional system consists of a Maxwell field interacting with a scalar field, leading to a deformation of the Bañados-Teitelboim-Zanelli black hole. We present the general formulas defining the black hole solutions in arbitrary dimensions in Lovelock theor…
On Accelerated Inertial Frames in Gravity and Electromagnetism
当带电绝缘球壳均匀加速时，内部会产生方向相反的电场。场的外部是均匀加速电荷的玻恩场，由偶极子修正。辐射产生。当加速度被具有1 + beta cos θ表面质量分布的外壳的几乎均匀的重力场抵消时，不同看法的玻恩场是静态的，并加入外壳外部的静态场;没有辐射产生。我们讨论这些现象的引力类似物。当一个巨大的球壳被加速时，内部未接触的测试质量经历均匀的重力场，并向周围的壳加速。在强引力制度，我们说明了这些影响使用的爱因斯坦-麦克斯韦方程组带电尘埃的精确构象解。我们考虑一个大质量的带电壳，其上的力由于几乎均匀的电场和引力场的平衡。这两个场在壳内都按壳内g_00与壳外g_00之比减小，自由测试粒子相对于静态观察者的加速度也相应减小。我们对这些效应给出了物理解释。
