Electromagnetic Energy-momentum Tensor Research Articles

Particle motion in the Einstein-Euler-Heisenberg rotating black hole spacetime

We study the motion of charged test particles and photons in the gravitational field of the rotating electrically charged Einstein-Euler-Heisenberg black hole solution. This describes a nonlinear electromagnetic generalization of the Kerr-Newman solution, which endows the vacuum with an effective dielectric constant. The orbits of photons are analyzed by means of the effective Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski pseudometric related to the geometrical metric and to the electromagnetic energy-momentum tensor. The QED induced modifications of the shape of the shadow are presented and discussed.

Dyonic black holes in the theory of two electromagnetic potentials. I

In the present paper we argue that the dyonic black hole spacetimes must be studied within the theory of two electromagnetic potentials, and we use the dyonic Reissner-Nordstr\"om solution to demonstrate that the field of the monopole magnetic charge is correctly described by the $t$-component of the dual electromagnetic potential. As a result, the Dirac string associated with the $\varphi$-component of the usual electromagnetic 4-potential becomes just a mathematical object, without any physical content, that arises in some calculations when one employs unsymmetrical representations of the electromagnetic field. We use three different, though equivalent, forms of the electromagnetic energy-momentum tensor to calculate the Komar mass of the Reissner-Nordstr\"om black hole, and in one case the Dirac string is linked to the magnetic charge, in another to the electric charge, while the third, symmetrical case, is string-free.

Fourth Rank Energy-Momentum Tensor

In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.

Is electromagnetic field momentum due to the flow of field energy?

Momentum and energy conservation require electromagnetic field momentum and energy to be treated as physically real, even in static fields. This motivates the conjecture that field momentum might be due to the flow of a relativistic mass density (defined as energy density divided by the square of the speed of light).This article investigates the velocity of such a mass flow and finds a conflict between two different definitions of it, both of which originally seem plausible if the flow is to be taken as real. This investigation is careful to respect the transformation rules of special relativity throughout.The paper demonstrates that the consensus definition of the flow velocity of electromagnetic energy is inconsistent with the transformation rules of special relativity, and hence is incorrect. A replacement flow velocity is derived which is completely consistent with those transformation rules.The conclusion is that these conflicting definitions of flow velocity cannot be resolved in a way that is consistent with special relativity and also allows electromagnetic field momentum density to be the result of relativistic mass flow. Though real, field momentum density cannot be explained as the flow of a relativistic mass density.As a byproduct of the study, it is also shown that there is a comoving system in which the electromagnetic energy-momentum tensor is reduced to a simple diagonal form, with two of its diagonal elements equal to the energy density and the other two diagonal elements equal to plus and minus a single parameter derived from the electromagnetic field values, a result that places constraints on possible fluid models of electromagnetism.

Optical forces on a cylinder induced by surface waves and the conservation of the canonical momentum of light.

Based on rigorous derivations using the electromagnetic energy-momentum tensor, we established a generic relationship between the longitudinal optical force (along the surface wave propagating direction) on a cylinder induced by surface waves and the energy flux of each surface mode supported on the interface between air and a lossless substrate possessing continuous translational symmetry along the longitudinal direction. The longitudinal optical force is completely attributed to the canonical momentum of light. Our theory is valid for generic types of surface waves and lays the theoretical foundation for the research and applications of optical manipulations by surface waves.

Energy-momentum tensor for the electromagnetic field in a dispersive medium

On the basis of a non-local Lagrangian for Maxwell equations in a dispersive medium, the energy-momentum tensor of the field is derived. We obtain the Field equations through variational methods and an extension of Noether theorem for a non-local Lagrangian is obtained as well. The electromagnetic energy-momentum tensor obtained in the general context is then specialized to the case of a field with slowly varying amplitude on a rapidly oscillating carrier.

Geodesic structure of the Euler-Heisenberg static black hole

We derive an electrically charged static black hole spacetime of the Einstein-Euler-Heisenberg theory, in terms of the Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski dual variables. This solution is a nonlinear electromagnetic generalization of the Reissner-Nordstr\om solution, and it is characterized by the mass $M$, the electric charge $Q$ of the black hole, and the Euler-Heisenberg nonlinear constant, which includes the fine structure constant $\ensuremath{\alpha}$. We study all possible equatorial trajectories of test particles. Moreover, the orbits of photons are analyzed by means of the effective Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski pseudometric related to the geometrical metric and to the electromagnetic energy-momentum tensor. The shape of the shadow of the black hole is also presented and discussed.

Reply to “Comment on ‘Analysis of recent interpretations of the Abraham-Minkowski problem’ ”

The Comment of M. Partanen and J. Tulkki [Phys. Rev. A {\bf 100}, 017801 (2019)] claims that my criticism expressed in Phys. Rev. A {\bf 98}, 043847 (2018) of the earlier paper of Partanen {\it et al.} [Phys. Rev. A {\bf 95}, 063850 (2017)] was incorrect. There are essentially three points involved here: (1) the first one regards the physical interpretation of the radiation pressure experiment of A. Kundu {\it et al.} [Sci. Rep. {\bf 7}, 42538 (2017)]. My mathematical analysis of this situation, although simple, was able to illustrate the main property of the experiment, namely that it showed the action from the radiation forces on the dielectric boundaries, and from the Lorentz force in the interior, but it had not any relationship to the Abraham-Minkowski momentum problem as was originally stated by the investigators. (2) The second point was my emphasis on the fact that in an electromagnetic pulse in a medium there cannot be an accompanying mechanical energy density of the same order of magnitude as the electromagnetic energy density itself. The electromagnetic wave carries with it a mechanical {\it momentum}, but not a mechanical {\it energy}. Here I illustrate this point by a simple numerical analysis. (3) When going to a relativistic formulation of the electromagnetic theory in matter, care must be taken to secure that fundamental conditions from field theory are satisfied. In particular, one cannot in general take the electromagnetic total energy and momentum of a radiation pulse to constitute a four-vector; such a property holds only if the electromagnetic energy-momentum tensor is divergence-free. For the Minkowski tensor this condition is satisfied, whereas for the Abraham tensor it is not.

Homothetic congruences in general relativity

The kinematical characteristics of distinct infalling homothetic fields are discussed by specifying the transverse subspace of their generated congruences to the energy–momentum deposit of the chosen gravitational system. This is pursued through the inclusion of the base manifold’s cotangent bundle in a generalized Raychaudhuri equation and its kinematical expressions. Exploiting an electromagnetic energy–momentum tensor as the source of non-gravitational effects, I investigate the evolution of the mentioned homothetic congruences, as they fall onto a Reissner–Nordström black hole. The results show remarkable differences to the common expectations from infalling congruences of massive particles.

Analysis of recent interpretations of the Abraham-Minkowski problem

The 100-year-long problem concerning the correct form of the electromagnetic energy-momentum tensor in continuous media (usually called the Abraham-Minkowski problem) continues to attract interest. We provide a critical analysis of interpretations presented in the literature on this topic recently, in two cases - one real experiment on radiation pressure A. Kundu {\it et al.}, Scient. Reports {\bf 7}, 42538 (2017), and one computer experiment M. Partanen {\it et al.}, Phys. Rev. A {\bf 95}, 063850 (2017).

Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields

We present a direct, geometric derivation of the generalized Smarr formula for the stationary axially symmetric black holes with nonlinear electromagnetic fields. The additional term is proven to be proportional to the integral of the trace of the electromagnetic energy-momentum tensor and can be written as a product of two conjugate variables. From the novel relation we can deduce all previously proposed forms of the generalized Smarr formula, which were derived only for the spherically symmetric black holes, and provide the lowest order quantum correction to the classical relation from the Euler–Heisenberg Lagrangian.

Poynting Theorem, Relativistic Transformation of Total Energy–Momentum and Electromagnetic Energy–Momentum Tensor

We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy–momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product \({\varvec{j}} \cdot {\varvec{E}}\) (where the current density \({\varvec{j}}\) and bound electric field \({\varvec{E}}\) are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy–momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy–momentum tensor.

Electromagnetic field and dynamical instability of collapse with CDTT model

This work investigates the dynamical instability of the relativistic self-gravitating collapsing fluids with electromagnetic field in Carrol–Duvvuri–Trodden–Turner (CDTT) f(R) model for spherical symmetric spacetime. In this scenario, we provide dynamical equations from the contracted Bianchi identities for the usual, effective dark source and electromagnetic energy–momentum tensor. The perturbation technique is used on the metric variables which ultimately induce perturbation on the selected f(R) model and on the physical variables. We conclude that higher curvature terms of CDTT model, density profile, electromagnetism and pressure anisotropy affect the range of instability at the Newtonian and post Newtonian regimes. It is worthwhile to mention here that our results approach asymptotically to general relativity solutions when δ→0.

FIELD EQUATIONS FOR SPACE–TIME–MATTER THEORY

In the present paper we obtain, in a covariant form, and in their full generality, the field equations in a relativistic general Kaluza–Klein space. This is done by using the Riemannian horizontal connection defined in [3], and some 4D horizontal tensor fields, as for instance: horizontal Ricci tensor, horizontal Einstein gravitational tensor field, horizontal electromagnetic energy–momentum tensor field, etc. Also, we present some inter-relations between STM theory and brane-world theory. This enables us to introduce in brane theory some electromagnetic potentials constructed by means of the warp function.

Continuity equations for bound electromagnetic field and the electromagnetic energy–momentum tensor

We analyze the application of the Poynting theorem to the bound (velocity-dependent) electromagnetic (EM) field and show that an often-used arbitrary elimination of the term of self-interaction in the product j·E (where j is the current density and E the electric field) represents, in general, an illegitimate operation, which leads to incorrect physical consequences. We propose correct ways of eliminating the terms of self-interaction from the Poynting theorem to transform it into the form that is convenient for problems with bound EM field, which yield the continuity equations for the proper EM energy density, the interaction part of EM energy density and the total EM energy density of bound fields, respectively. These equations indicate the incompleteness of the common EM energy–momentum tensor, and in our analysis, we find a missed term in its structure, which makes its trace non-vanished. Some implications of these results are discussed, in particular, in view of the notion of EM mass of charged particles.

ELECTROMAGNETIC CASIMIR EFFECT IN WEDGE GEOMETRY AND THE ENERGY-MOMENTUM TENSOR IN MEDIA

The wedge geometry closed by a circular-cylindrical arc is a nontrivial generalization of the cylinder, which may have various applications. If the radial boundaries are not perfect conductors, the angular eigenvalues are only implicitly determined. When the speed of light is the same on both sides of the wedge, the Casimir energy is finite, unlike the case of a perfect conductor, where there is a divergence associated with the corners where the radial planes meet the circular arc. We advance the study of this system by reporting results on the temperature dependence for the conducting situation. We also discuss the appropriate choice of the electromagnetic energy-momentum tensor.

Comment on “Casimir force acting on magnetodielectric bodies embedded in media”

In a recent paper [Raabe and Welsch, Phys. Rev. A 71, 013814 (2005)] an electromagnetic energy-momentum tensor is suggested as an alternative to the Abraham-Minkowski tensor and is applied to calculations of Casimir forces in planar geometries. We argue that the universality of the suggested tensor is doubtful; application of the Raabe-Welsch theory to a simple example in classical electrodynamics shows that their proposed tensor is unable to describe the situation in a simple way. We also show that modified Casimir forces acting on the cavity medium as prescribed by these authors suffer from problems of definiteness and peculiar properties which call for experimental support before this theory can be regarded as acceptable.

Maxwell's equations in Minkowski's world: their premetric generalization and the electromagnetic energy-momentum tensor

In the special theory of relativity, Lorentz invariance is extended in Minkowski spacetime from ideal inertial observers to actual observers by means of the hypothesis of locality, which postulates that accelerated observers are always pointwise inertial. A critical examination of the locality assumption reveals its domain of validity: it is true for pointwise coincidences, but is in conflict with wave-particle duality. To remedy this situation, a nonlocal theory of accelerated systems is presented that reduces to the standard theory in the limit of small accelerations. Some of the main consequences of nonlocal special relativity are briefly outlined.

From Rindler space to the electromagnetic energy-momentum tensor of a Casimir apparatus in a weak gravitational field

This paper studies two perfectly conducting parallel plates in the weak gravitational field on the surface of the Earth. Since the appropriate line element, to first order in the constant gravity acceleration $g$, is precisely of the Rindler type, we can exploit the formalism for studying Feynman Green functions in Rindler spacetime. Our analysis does not reduce the electromagnetic potential to the transverse part before quantization. It is instead fully covariant and well suited for obtaining all components of the regularized and renormalized energy-momentum tensor to arbitrary order in the gravity acceleration $g$. The general structure of the calculation is therefore elucidated, and the components of the Maxwell energy-momentum tensor are evaluated up to second order in $g$, improving a previous analysis by the authors and correcting their old first-order formula for the Casimir energy.

Response to ‘On negative refraction in classical vacuum’

An analysis [McCall, M.W. J. Mod. Opt. 2007, 54, 119–128] based on the electromagnetic energy-momentum tensor, to explore the prospects for negative-phase-velocity (NPV) propagation in gravitationally affected vacuum, did not consider (i) the total energy-momentum tensor and (ii) the global perspective of curved spacetime. Also, the appearance of NPV was wrongly attributed to a change in signature of the spacetime metric.