Unified equation of motion of a test charge in electromagnetic and gravitational fields

This work starts by generalizing in a gravitational field the fundamental quantum mechanical commutation relations between the coordinates of a charged test particle and its momentum. Assuming that the components of the momentum of this test charge obey a noncommutative algebra in the presence of an electromagnetic field, it is proved that the commutator can be identified with the electromagnetic field tensor. Using these results, the equation of motion of this charged object in the presence of both the electromagnetic and gravitational fields is derived from their field equations. In this work, the laws of motion of a particle in the electromagnetic and gravitational fields has been unified with the field equations. Although the field equations themselves are not directly unified, this work strongly suggests that the scheme may act as a possible framework for the unification of at least gravitational and electromagnetic interactions.     

Orthonormal tetrads and the charged fluid in general relativity

A space-time filled with the self-gravitating charged fluid with constant electric permitivity and constant magnetic permeability is investigated. On expressing the stress-energy tensor in terms of an orthonormal tetrad, the equations of motion and Maxwell equations are formulated. In case of the geodesic flow, the conditions for divergence-free electric and magnetic fields are obtained. It is shown that the space-time permeated by the charged fluid with the electric field orthogonal to the magnetic one is embedded in 5-dimensional flat class-one space-time if and only if the electromagnetic energy flux vector vanishes.     

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.     

Electrodynamics in an expanding universe

An algebraic form of the energy momentum tensor of the electromagnetic field is derived in terms of two scalars and two mutually orthogonal vector fields. Upon inserting this tensor into the field equations, solutions of the co-determined Einstein-Maxwell equations are obtained. The line element used is that corresponding to a conformal flat universe, whose form is then uniquely determined by the field equations. The case of a charged fluid is also considered and it is found that the particular form of the velocity field chosen limits the choice of the possible equation of state connecting the pressure and density distributions.     

Microscopic derivation of hydrodynamic balance equations in the presence of an electromagnetic field

Using field-theoretic methods we derive balance equations for a charged fluid in an external electromagnetic field the effects of which are included by minimal coupling. An infinite hierarchy of balance equations for tensor operators is derived. A macroscopic velocity field is introduced by a unitary transformation on the field operators. Suitable statistical averages in the local equilibrium approximation yield macroscopic balance equations. The significance of new terms is discussed.     

Numerical Simulation of Shear-Horizontal-Wave-Induced Electromagnetic Field in Borehole Surrounded by Porous Formation

Seismoelectric fieM excited by purely torsional loading applied directly to the borehole wall is considered. A brief formulation and some computed waveforms show the advantage of using shear-horizontal （SH） transverseelectric （TE） seismoelectric waves logging to measure shear velocity in a fluid-saturated porous formation. By assuming that the acoustic field is not influenced by its induced electromagnetic field due to seismoeleetric effect, the coupling governing equations for electromagnetic field are reduced to Maxwell equations with a propagation current source. It is shown that this simplification is valid and the borehole seismoelectric conversion efficient is mainly dependent on the electrokinetic coupling coefficient. The receivers to detect the conversion electromagnetic field and to obtain shear velocity can be set in the borehole fluid in the SH-TE seismoelectric wave log.     

Gravitational collapse of charged scalar fields

In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the Maxwell–Klein–Gordon sector are derived in the \(3+1\) formalism, and coupled to gravity by means of the stress–energy tensor of these fields. To solve consistently the full system we employ a generalized Baumgarte–Shapiro–Shibata–Nakamura formulation of General Relativity that is adapted to spherical symmetry. We consider two sets of initial data that represent a time symmetric spherical thick shell of charged scalar field, and differ by the fact that one set has zero global electrical charge while the other has non-zero global charge. For compact enough initial shells we find that the configuration doesn’t disperse and approaches a final state corresponding to a sub-extremal Reissner–Nördstrom black hole with \(|Q| . By increasing the fundamental charge of the scalar field \(q\) we find that the final black hole tends to become more and more neutral. Our results support the cosmic censorship conjecture for the case of charged matter.     

Electromagnetic effects on complexity factor for static cylindrical system

This paper investigates the phenomenon of complexity factor for static charged anisotropic cylindrical configuration. We formulate some basic equations such as Einstein–Maxwell field equations, Tolman–Opphenheimer–Volkoff equation and mass equation. Further, the orthogonal splitting of the Riemann tensor is used to obtain the structure scalars that lead to the complexity factor. Finally, we investigate some theoretical models with vanishing complexity condition. It is found that the complexity of the system increases for α ≤ 1 in the presence of the electromagnetic field.     

读“等效的磁荷观点”有感

文章在假想的“磁荷世界”中修改了麦克斯韦方程组和洛伦兹力公式.由磁的库仑定律出发,并根据磁荷与电荷产生的电磁场的等效性,得到真空中静磁场的高斯定理和环路定理.仿照“电荷世界”中的电流定义了磁流强度,又根据磁场的相对论变换,由毕奥—萨伐尔定律和法拉第电磁感应定律得到稳恒电场D的高斯定理和环路定理.     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

Regular models with quadratic equation of state

We provide new exact solutions to the Einstein–Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein–Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.     

Complexity factor for charged spherical system

In this paper, we study the complexity factor for a charged anisotropic self-gravitating object. We formulate the Einstein–Maxwell field equations, Tolman–Opphenheimer–Volkoff equation, and the mass function. We form the structure scalars by the orthogonal splitting of the Riemann tensor and then find the complexity factor with the help of these scalars. Finally, we investigate some astrophysical objects for the vanishing of complexity condition. It is found that the presence of the electromagnetic field decreases the complexity of the system.     

Charged fluids with symmetries

We investigate the role of symmetries for charged perfect fluids by assuming that spacetime admits a conformal Killing vector. The existence of a conformal symmetry places restrictions on the model. It is possible to find a general relationship for the Lie derivative of the electromagnetic field along the integral curves of the conformal vector. The electromagnetic field is mapped conformally under particular conditions. The Maxwell equations place restrictions on the form of the proper charge density.     

Complementary aspects of gravitation and electromagnetism

A convention with regard to geometry, accepting nonholonomic aether motion and coordinate-dependent units, is always valid as an alternative to Einstein's convention. Choosing flat spacetime, Newtonian gravitation is extended, step by step, until equations closely analogous to those of Einstein's theory are obtained. The first step, demanded by considerations of inertia, is the introduction of a vector potential. Treating the electromagnetic and gravitational fields as real and imaginary components of a complex field (gravitational mass being treated as imaginary charge), the Maxwell stress-momentum-energy tensor for the complex field is then used as the source for both fields. The spherically symmetric solution of these unified field equations describes the electron. Third, effects arising from motion of aether fluid with respect to the artificial reference systems of flat spacetime are included. On the grounds that attraction between likes and repulsion between likes are, a priori, equally possible, it is suggested that gravitational and electromagnetic phenomena should enjoy equal status. This can be achieved on the scale of an infinite cosmos by introducing a hierarchy of isolated systems, each of which is a universe when viewed internally and an elementary particle when viewed externally. A universe (defined by the Hubble radius), an electron, and a neutrino are three consecutive isolated systems of the hierarchy. Implied is the existence of antiuniverses where gravitational mass has opposite sign and antimatter predominates. Remarkable relationships between physical constants emerge.     

Test of a model coupling of electromagnetic and gravitational fields by using high-frequency gravitational waves

Models of the coupling of electromagnetic and gravitational fields have been studied extensively for many years. In this paper,we consider the coupling between the Maxwell field and the Weyl tensor of the gravitational field to study how the wavevector of the electromagnetic wave is affected by a plane gravitational wave. We find that the wavevector depends upon the frequency and direction of polarization of the electromagnetic waves, the parameter that couples the Maxwell field and the Weyl tensor, and the angle between the direction of propagation of the electromagnetic wave and the coordinate axis. The results show that this coupling model can be tested by the detection of high-frequency gravitational waves.     

Corrections to the Thomson cross section caused by relativistic effects and by the presence of the drift velocity of a classical charged particle in the field of a monochromatic plane wave

An approach to the solution of the relativistic problem of the motion of a classical charged particle in the field of a monochromatic plane wave with an arbitrary polarization (linear, circular, or elliptic) is proposed. It is based on the analysis of the 4-vector equation of motion of the charged particle together with the 4-vector and tensor equations for the components of the electromagnetic field tensor of a monochromatic plane wave. This approach provides analytical expressions for the time-averaged square of the 4-acceleration of the charge, as well as for the averaged values of any quantities periodic in the time of the reference frame. Expressions for the integral power of scattered radiation, which is proportional to the time-averaged square of the 4-acceleration of the charge, and for the integral scattering cross section, which is the ratio of the power of scattered radiation to the intensity of incident radiation, are obtained for an arbitrary inertial reference frame. An expression for the scattering cross section, which coincides with the known results at the circular and linear polarizations of the incident waves and describes the case of elliptic polarization of the incident wave, is obtained for the reference frame where the charged particle is on average at rest. An expression for the scattering cross section including relativistic effects and the nonzero drift velocity of a particle in this system is obtained for the laboratory reference frame, where the initial velocity of the charged particle is zero. In the case of the circular polarization of the incident wave, the scattering cross section in the laboratory frame is equal to the Thompson cross section.     

Effects of electromagnetic field on energy density inhomogeneity in self-gravitating fluids

This paper is devoted to study the effects of electromagnetic field on the energy density inhomogeneity in the relativistic self-gravitating fluids for spherically symmetric spacetime. Two important equations of the Weyl tensor are formulated which help to analyze the energy density inhomogeneity in this scenario. We investigate two types of fluids, i.e., non-dissipative and dissipative. The non-dissipative fluid further includes dust, locally isotropic, and locally anisotropic charged fluids. We explore the effects of different factors on energy density inhomogeneity in all these cases, in particular, the effect of charge.     

电磁场的复矢量表示

在麦克斯韦方程组及洛伦兹力密度公式基础上引入电磁场复矢量,讨论了电磁场普遍规律的新公式,包括对复矢量电磁场的建立,电荷守恒定律,能量守恒定律,电磁场矢势与标势,电磁场动量、能量、张量、相对论协变性等的研究,并和电动力学相比较,得出一些结论.     

Generating physically realizable stellar structures via embedding

In this work we present an exact solution of the Einstein–Maxwell field equations describing compact charged objects within the framework of classical general relativity. Our model is constructed by embedding a four-dimensional spherically symmetric static metric into a five-dimensional flat metric. The source term for the matter field is composed of a perfect fluid distribution with charge. We show that our model obeys all the physical requirements and stability conditions necessary for a realistic stellar model. Our theoretical model approximates observations of neutron stars and pulsars to a very good degree of accuracy.