Alexander A. Chernitskii
We consider the unification problem for the gravitational and electromagnetic interactions and its possible solution on the basis of the existence of an effective Riemannian space in nonlinear electrodynamics
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Within the context of a $5D$ space-time, we construct a unified theory of gravity and electromagnetism from which the Einstein field equations and Maxwell equations emerge, with homogenous Maxwell equations appearing naturally. We also introduce a well-defined five dimensional energy-momentum tensor consistent with our unification scheme. A correction term appears in Maxwell equations which can be used to explain the recently discovered galactic magnetic fields.
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.
It is shown that unification of gravity and electromagnetism can be achieved using an affine non-symmetric connection $Γ^λ_{μν} \neq Γ^λ_{νμ}$ and $Γ_μ= Γ^λ_{[μλ]}\neq 0$. $Γ_μ$ is shown to be the source of the electromagnetic field. This unification is based on {\em projective invariance} which is broken by matter fields, opening up the possibility of a unified theory of all forces in which gravity emerges as a classical field.
Principles of Maxwell, Lorentz, Milne, Dirac and Feynman are combined to unify gravity with electromagnetism.
Unification of gravity and electromagnetism based on a theory with an affine non-symmetric connection $Γ^λ_{μν} \neq Γ^λ_{νμ}$ and $Γ_μ= Γ^λ_{[μλ]}\neq 0$, proposed by S. N. Bose in 1953, is revisited in the context of modern developments in high energy physics. It is shown that electrogravity unification can be achieved at a {\em premetric} stage, and that this unification based on {\em projective invariance} is broken by matter fields, opening up the possibility of a unified theory of all forces in which gravity emerges as a classical field. The theory predicts $α_{sym} = \frac{1}{9}$ in the…
We show in the framework of Pfaff systems theory, the functional dependences of the general analytic solutions of a suitable system of involutive differential equations describing the differences between the analytic solutions of the conformal and "Poincaré" Lie equations. Then we ascribe to the infinitesimal variations of the parametrizing functionals some physical meanings as the electromagnetic and gravitation potentials. We also deduce their corresponding fields of interactions together with the differential equations they must satisfy. Then we discuss on various possible physical interpre…
H. Akbar-Zadeh has recently proposed (J Geom Phys 17 (1995) 342) a new geometric formulation of Einstein-Maxwell system with source in terms of what are called "Generalized Einstein manifolds". We show that, contrary to the claim, Maxwell equations have not been derived in this formulation and that, the assumed equations can be identified only as source-free Maxwell equations in the proposed geometric set up. A genuine derivation of source-free Maxwell equations is presented within the same framework. We draw a conclusion that the proposed unification scheme can pertain only to source-free sit…
The phenomenological consequences of unification of Einstein gravity and electromagnetism in an early phase of a Machian universe with a very small and uniform electrical charge density $ρ_q$ are explored. A form of the Strong Equivalence Principle for unified electrogravity is first formulated, and it immediately leads to (i) the empirical Schuster-Blackett law relating the magnetic moments and angular momenta of neutral astronomical bodies, (ii) an analogous relation between the linear acceleration of neutral massive bodies and associated electric fields, (iii) gravitational lensing in exces…
The space-time curvature carried by electromagnetic fields is discovered and a new unification of geometry and electromagnetism is found. Curvature is invariant under charge reversal symmetry. Electromagnetic field equations are examined with De Rham co homology theory. Radiative electromagnetic fields must be exact and co exact to preclude unobserved massless topological charges. Weyl's conformal tensor, here called ``the gravitational field'', is decomposed into a divergence-free non-local piece with support everywhere and a local piece with the same support as the matter. By tuning a local …
We first review the cosmological constant problem, and then mention a conjecture of Feynman according to which the general relativistic theory of gravity should be reformulated in such a way that energy does not couple to gravity. We point out that our recent unification of gravitation and electromagnetism through a symmetric tensor has the property that the free electromagnetic energy and the vacuum energy do not contribute explicitly to the curvature of spacetime just like the free gravitational energy. Therefore in this formulation of general relativity, the vacuum energy density has its ve…
Although the wish to unify theories into something more fundamental is omnipresent and compelling, nonetheless, in a sense, theories must first be unifiable. The reasons for the success of the unification of electricity and magnetism into a theory of electromagnetism are contrasted with the reasons for the failure of the Einstein-Maxwell unification of gravitation and electromagnetism and the attempts of quantum gravity to unify Einstein's theory of gravity with quantum field theory. The difference between a unification of two theories, a concatenation of them, and the existence of a formal an…
The classical concept of "mass density" is not fundamental to the quantum theory of matter. Therefore, mass density cannot be the source of gravitation. Here, we treat electromagnetic energy, momentum, and stress as its source. The resulting theory predicts that the gravitational potential near any charged elementary particle is many orders of magnitude greater than the Newtonian value.
We presented a model for unification of electricity and gravity. We have found a consistent description of all physical quantities pertaining to the system. We have provided limiting values for all physical values. These values are neither zero nor infinity. Our universe is described at all times by the four dimensional constants $c, \hbar, k, G$ only. The remnant of vacuum remains at all epochs with different values. The present cosmological puzzles are justified as due to the consequences of cosmic quantization developed in this work.
We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, 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 …
We argue that the starting point of Kaluza's idea of unifying electrodynamics and gravity was the analogy between gravitation and electromagnetism which was pointed out by Einstein and Thirring. It seems that Kaluza's attention was turned to this point by the three papers on the Lense-Thirring effect and the analogy between gravitation and electromagnetism which were published a short time before Kaluza's paper was submitted. We provide here an English translation of the third of these papers.
Using the weak field approximation, we can express the theory of general relativity in a Maxwell-type structure comparable to electromagnetism. We find that every electromagnetic field is coupled to a gravitoelectric and gravitomagnetic field. Acknowledging the fact that both fields originate from the same source, the particle, we can express the magnetic and electric field through their gravitational respective analogues using the proportionality coefficient k. This coefficient depends on the ratio of mass and charge and the ratio between the electromagnetic and gravitic-gravitomagnetic permi…
In this talk the description of gauge theories associated with internal symmetries is extended to the case in which the symmetry group is the space-time translation group (recovering Einstein's theory) using the standard jet-bundle formalism. We also reformulate these theories introducing the idea of jet-gauge and jet-diffeomorphism groups. Finally, we attempt to a simple, yet non-trivial, mixing of gravity and electromagnetism (or more general internal interaction) by turning to gauge symmetry a central extension of the Poincare group.
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.
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.
The Maxwell field of a charge e which experiences an impulsive acceleration or deceleration is constructed explicitly by subdividing Minkowskian space-time into two halves bounded by a future null-cone and then glueing the halves back together with appropriate matching conditions. The resulting retarded radiation can be viewed as instantaneous electromagnetic bremsstrahlung. If we similarly consider a spherically symmetric, moving gravitating mass, to experience an impulsive deceleration, as viewed by a distant observer, then this is accompanied by the emission of a light-like shell whose tota…
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…
Aharonov-Bohm Effects for Electromagnetism and Gravity in Four-Dimensional Spacetime
该研究构建四维时空引力Aharonov-Bohm效应的几何框架，推导量子态和乐变换，证明牛顿近似下引力相移与电磁相移同构，确立引力规范结构量子可观测性并为原子干涉实验提供理论支持。
This work is focused on the theory of Gravitoelectromagnetism (GEM). In the first part of this work we present a brief review of gravitoelectromagnetism, we locate and discuss all the problems which appear in this approach. We also try to avoid these problems by proposing new approaches in which we use the additional degrees of freedom of the gravitational field. In the second part of this work, we review our previous work regarding the construction of a tensorial theory, using the formalism of General Relativity, which aims to describe the true electromagnetism. We also extend this theory in …
Revised translation of Kaluza's historic 1921 paper, "Zum Unitätsproblem der Physik," on 5-dimensional spacetime, used to unify gravity and electromagnetism. This version is based, in part, on a 1984 translation provided by T. Muta, but revised and formatted using LaTeX to closely match the original paper in appearance and pagination. Kaluza's original notation is restored.
Electromagnetism in Curved Spacetimes: Coupling of the Doppler and Gravitational Redshifts
本文在广义相对论框架下推广电磁理论，利用法拉第张量和爱因斯坦场方程描述弯曲时空中的电磁辐射，并推导了引力红移与多普勒频移的联合效应公式。
There is a deep interrelationship of the General Theory of Relativity and weak interactions in the model of Expansive Nondecelerative Universe. This fact allows an independent determination of the mass of vector bosons Z and W, as well as the time of separation of electromagnetic and weak interactions.
Refined Perspectives on the Kerr-Schild Double Copy:Harmonizing Gravity and Electromagnetism in Metric Formulations
本文研究关联引力与电磁学的Kerr-Schild double copy对偶性，展示四维爱因斯坦真空解向麦克斯韦解的转换方法，验证其在多类黑洞解推导等场景的应用，并分析特定对称性下的相关影响。
Possible geometric frameworks for a unified theory of gravity and electromagnetism are investigated: General relativity is enlarged by allowing for an arbitrary complex linear connection and by constructing an extended spinor derivative based on the complex connection. Thereby the spacetime torsion not only is coupled to the spin of fermions and causes a four-fermion contact interaction, but the non-metric vector-part of torsion is also related to the electromagnetic potential. However, this long-standing relation is shown to be valid only in a special U(1) gauge, and it is a formal consequenc…
A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase symmetry of electromagnetism. The reversed sign for the gravitational coupling is obtained by means of the pseudoscalar of the underlying complex Clifford algebra.
Quantum Gravitational Corrections to Electromagnetism And Backreaction
本文在微扰广义相对论有效场论框架下研究量子引力对电磁学的修正及反作用，推导了量子修正的麦克斯韦方程、诱导耦合、光子传播子模求和及暴胀子有效力，并分析其对再加热的影响。
Stringent Constraints on Gravitational Wave Signatures of Dark Electromagnetism in Neutron Star Binaries
研究通过分析中子星双星系统中暗电磁现象的引力波特征，发现矢量力的排斥性质对隐藏扇区粒子的耦合施加了严格约束，表明当前引力波观测难以探测此类现象。
Electromagnetic field produced by magnetic multipoles in hyperbolic motion is derived and compared with electromagnetic field produced by electric multipoles in hyperbolic motion. The resulting fields are related by duality symmetry. Radiative properties of these solutions are demonstrated. In the second part an analogous, uniformly accelerated source of gravitational radiation is studied, within exact Einstein's theory. Radiative characteristics of the corresponding solution as flux of the radiation and the total mass-energy of the system are calculated and graphically illustrated.
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along with Gravitation, at the time it gives a geometric foundation for the stress-energy tensor of continuous matter. The geometric-invariance principle under this integration is exposed and the resulting field equations are obtained. The theory is developed over the tangent space of a four-dimensional real manifold and the generators become those from the Homogeno…
We develop a theoretical framework that allows us to compare electromagnetism and gravitation in a fully covariant way. This new scenario does not rely on any kind of approximation nor associate objects with different operational meaning as it's sometime done in the literature. We construct the electromagnetic analogue to the Riemann and Weyl tensors and develop the equations of motion for these objects. In particular, we are able to identify precisely how and in what conditions gravity can be mapped to electrodynamics. As a consequence, many of the gemometrical tools of General Relativity can…
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…
The response of the ultrarelativistic particle with spin in a Schwarzschild field to the gravitomagnetic components as measured by the comoving observer is investigated. The dependence of the particle's spin-orbit acceleration on the Lorentz γ- factor and the spin orientation is studied. The concrete circular ultrarelativistic orbit of radius r=3m is considered as a partial solution of the Mathisson-Papapetrou equations and as the corresponding high-energy quantum state of the Dirac particle. Numerical estimates for protons and electrons near black holes are given. A tendency of gravitational …
The objective of a SEE mission is to support development of unification theory by carrying out sensitive gravitational tests capable of determining whether various alternative theories are compatible with nature. Gravitation is a key "missing link" in unification theory. Nearly all unification theories incorporate gravity at a fundamental level, and therefore precise measurements of gravitational forces will place important constraints on unification theories. Ground-based gravitational measurements to the accuracy required are impossible due to the many sources of noise present in the terrest…
We deal with the gravitational theory relevant to gravito-electromagnetism (GEM) exactly. It is shown that the theory can be decomposed in terms of two sectors of Abelian gauge field theories. The two sectors dominate the whole action in an inverse way, showing a sign of strong-weak duality.
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to emulate electromagnetic gauge transformations under substitutions belonging to the gauge symmetry group of perturbative gravitation. These definitions have the advantage that on a flat background, with the aid of a covariantly constant timelike vector field, a subset of the linearised gravitational field equations can be written in a form that is fully anal…
On a field tensor for gravity and electromagnetism
本文证明三秩Lanczos型张量场可用于描述相对论性电磁与引力效应，将其不可约分解识别为引力与电磁场，并提出一组散度方程作为场方程。
The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the Einstein-Maxwell Lagrangian in the metric formulation. We show that the sum of the two affine Lagrangians is dynamically inequivalent to the sum of the analogous Lagrangians in the metric-affine/metric formulation. We also show that s…
If gravitation and electromagnetism are both described in terms of a symmetric metric tensor, then the deflection of an electron beam by a charged sphere should be different from its deflection according to the Reissner-Nordström solution of General Relativity. If such a unified description is true, the equivalence principle for the electric field implies that the photon has a nonzero effective electric charge-to-mass ratio and should be redshifted in an electric field and be deflected in a magnetic field. Experiments to test these predictions are proposed.
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…
We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar's new variables. We construct the connection and loop representations and analyze the space of states. In the loop representation, the wavefunctions depend on two loops, each of them carrying information about both gravitation and electromagnetism. We find that the Chern-Simons form and the Jones Polynomial play a role in the model.
The unification of quantum field theory and general relativity is a fundamental goal of modern physics. In many cases, theoretical efforts to achieve this goal introduce auxiliary gravitational fields, ones in addition to the familiar symmetric second-rank tensor potential of general relativity, and lead to nonmetric theories because of direct couplings between these auxiliary fields and matter. Here, we consider an example of a metric-affine gauge theory of gravity in which torsion couples nonminimally to the electromagnetic field. This coupling causes a phase difference to accumulate between…
In the purely affine formulation of gravity, the gravitational field is represented by the symmetric part of the Ricci tensor of the affine connection. The classical electromagnetic field can be represented in this formulation by the second Ricci tensor of the connection. Such a construction is dynamically equivalent to the sourceless Einstein-Maxwell equations. We generalize this construction to the case with sources, represented by the derivative of the affine Lagrangian density with respect to the connection. We show that the Maxwell equations with sources emerge for the simplest affine Lag…
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…
In Einstein's general relativity, geometry replaces the concept of force in the description of the gravitation interaction. Such an approach rests on the universality of free-fall--the weak equivalence principle--and would break down without it. On the other hand, the teleparallel version of general relativity, a gauge theory for the translation group, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. It is shown that, similarly to the Maxwell's description of electromagnetism, the teleparallel gauge approach provi…
The covariance group for general relativity, the diffeomorphisms, is replaced by a group of coordinate transformations which contains the diffeomorphisms as a proper subgroup. The larger group is defined by the assumption that all observers will agree whether any given quantity is conserved. Alternatively, and equivalently, it is defined by the assumption that all observers will agree that the general relativistic wave equation describes the propagation of light. Thus, the group replacement is analogous to the replacement of the Lorentz group by the diffeomorphisms that led Einstein from speci…
Recently much controversy has been shed on BICEP 2 experiments for the concerning this validity or not and a possible set of new experiments to detect primordial inflation and gravitational waves. Since gravitational waves imply the existence of primordial magnetic fields in this context, C Bonvin, R Durrer and R Marteens [Phys Rev Lett (2014)] have tried to associate the presence of primordial magnetic fields to BICEP 2 by making use of CMB tensor modes. Here we show that by considering torsion dilatonic lagrangean one obtains cosmological magnetic fields of the order of $B\sim{10^{-10}G}$ wh…
In this paper we investigate the gravitational vacuum stars which called gravastars in the non-minimally coupled models with electromagnetic and gravitational fields. We consider two non-minimal models and find the corresponding spherically symmetric exact solutions in the interior of the star consisting of the dark energy condensate. Our models turn out to be Einstein-Maxwell model at the outside of the star and the solutions become the Reissner-Nordstr{ö}m solution. The physical quantities of these models are continuous and non-singular in some range of parameters and the exterior geometry c…
We develop and apply a fully covariant 1+3 electromagnetic analogy for gravity. The free gravitational field is covariantly characterized by the Weyl gravito-electric and gravito-magnetic spatial tensor fields, whose dynamical equations are the Bianchi identities. Using a covariant generalization of spatial vector algebra and calculus to spatial tensor fields, we exhibit the covariant analogy between the tensor Bianchi equations and the vector Maxwell equations. We identify gravitational source terms, couplings and potentials with and without electromagnetic analogues. The nonlinear vacuum Bia…
Electromagnetism in spacetime can be treated in terms of an analogue linear dielectric medium. In this paper, we discuss the gravitational analogue of the linear magnetoelectric effect, which can be found in multiferroic materials. While this is known to occur for metrics with non-zero mixed components, we show how it depends on the choice of spatial formalism for the electromagnetic fields, including in differences in tensor weight, and also on the choice of coordinate chart. This is illustrated for Langevin-Minkowski, four charts of Schwarzschild spacetime, and two charts of pp gravitational…
Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer cohomology of Lie equations. Then, from the sophisticated non-linear Spencer complex of the Poincaré and conformal Lie pseudogroups, we build up a non-linear relative complex assigned to a gauge sequence for electromagnetic and gravitational potentials and fields. Then, using a conformally equivariant Lagrangian density, we deduce, first, the two first steps of its corresponding Janet complex and second, t…
Unified theory of gravitational interactions and electromagnetic interactions is discussed in this paper. Based on gauge principle, electromagnetic interactions and gravitational interactions are formulated in the same manner and are unified in a semi-direct product group of U(1) Abel gauge group and gravitational gauge group.
We show that it is possible to formulate the classical Einstein-Maxwell-Dirac theory of spinors interacting with the gravitational and electromagnetic fields as the Einstein-Cartan-Kibble-Sciama theory with the Ricci scalar of the traceless torsion, describing gravity, and the torsion trace acting as the electromagnetic potential.
The event GW150914 was the first historical detection of gravitational waves (GWs). The emergence of this ground-breaking discovery came not only from incredibly innovative experimental work, but also from a centennial of theoretical analyses. Many such analyses were performed by pioneering scientists who had wandered through a wild territory of mathematical laws. We explore such wandering and explain how it may impact the grand goal of unification in physics.
Unification of Conformal and Fuzzy Gravities with Internal Interactions - study of their behaviour in low energies and possible signals in the detection of Gravitational Waves
本文基于弯曲流形切群与流形维度可不同、两类引力均有规范理论表述两项事实，通过拓展四维切群构建含内部相互作用的共形引力与模糊引力统一方案，并分析其低能行为与引力波探测相关信号。
Gravitational Wave Signals in a Promising Realization of SO(10) Unification
研究非超对称大统一模型中SO(10)分阶段破缺产生的引力波信号，分析一阶相变及原初等离子体背景引力波，指出实验灵敏度尚需新型探测器技术提升。
In this paper we first show that any coupled system consisting of a gravitational plus a free electromagnetic field can be described geometrically in the sense that both Maxwell equations and Einstein equation having as source term the energy-momentum of the electromagnetic field can be derived from a geometrical Lagrangian proportional to the scalar curvature R of a particular kind of Riemann-Cartan spacetime structure, where those fields are identified as geometrical objects of the structure. We show moreover that the contorsion tensor of the particular Riemann-Cartan spacetime structure of …
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