Analog gravity from electrodynamics in non-linear media

Physical Review D, 2002

Working with electrodynamics in the geometrical optics approximation we derive the expression representing an effectively curved geometry which guides the propagation of electromagnetic waves in material media whose physical properties depend on an external electric field. The issue of birefringence is addressed, and the trajectory of the extraordinary ray is explicitly worked out. Quite general curves are obtained for the path of the light ray by suitably setting an electric field.

2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), 2019

In this paper we propose to solve approximately using perturbation theory, Maxwell’s equations in general relativity ie in curved space-time (that describes gravitational effects ofmatter on the electromagnetic field) taking in addition account of the fact that the medium may be nonlinear, inhomogeneous and anisotropic that is described by a electromagnetic field dependent permittivity – permeability -conductivity tensor. We also propose a method for estimating under such circumstances, ie gravitational effects & inhomogeneity anisotropicity & nonlinearity of the medium into account, the surface current density induced on an antenna when an electromagnetic field is incident upon it. The entire formalism is based on the tensor calculus and covariant differentiating fundamental to the general theory of relativity.

 Abstract—This article discusses some of the issues concerning the interaction of material particles with electromagnetic radiation. The investigation is based on solution of the Maxwell-Einstein equations. Basically four issues were explored: (i) A contribution in the ponderomotive force acting onto the probe particle which is determined by the curvature of space-time metric induced by the spherical electromagnetic wave; (ii) A metric which corresponds to the gravitational field created together by a massive source and an electromagnetic wave; (iii) A stability of the electromagnetic vacuum near space-time horizons; (iv) A real topology of space-time. The two last questions involve the non-wave solutions of the Maxwell-Einstein equations. We discuss also the loss of information accompanying the process of transformation a converging spherical electromagnetic wave into a diverging one.

1983

The Maxwell equations in a weak gravitational field are reduced to a single scalar wave equation. An analogous result is also obtained for a slowly varying gravitational field of arbitrary intensity that is accurate to the second-order terms with respect to the photon wavelength. Calculations are made of the refractive index and of the phase and group velocities of the electromagnetic waves.

2011

We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the electromagnetic waves.

2016

We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the electromagnetic waves. Summary-Introduction-1. On a consequence of the fact that the light-rays are null geodesics in any spacetime manifold.-2. The Maxwell equations of an electromagnetic wave are a consequence of the Einstein equations for the same wave.-2bis. An example.-3. A result analogous to that of sect.2 holds in the linear version of GR.-3bis, 3ter. An example.-4. A final remark.-Appendix.

Journal of Physics A: Mathematical and Theoretical, 2007

By recognising that stress-energy-momentum tensors are fundamentally related to gravitation in spacetime it is argued that the classical electromagnetic properties of a simple polarisable medium may be parameterised in terms of a constitutive tensor whose properties can in principle be determined by experiments in non-inertial (accelerating) 1 frames and in the presence of weak but variable gravitational fields. After establishing some geometric notation, discussion is given to basic concepts of stress, energy and momentum in the vacuum where the useful notion of a drive form is introduced in order to associate the conservation of currents involving the flux of energy, momentum and angular momentum with spacetime isometries. The definition of the stress-energy-momentum tensor is discussed with particular reference to its symmetry based on its role as a source of relativistic gravitation. General constitutive properties of material continua are formulated in terms of spacetime tensors including those that describe magneto-electric phenomena in moving media. This leads to a formulation of a self-adjoint constitutive tensor describing, in general, inhomogeneous, anisotropic, magneto-electric bulk matter in arbitrary motion. The question of an invariant characterisation of intrinsically magneto-electric media is explored. An action principle is established to generate the phenomenological Maxwell system and the use of variational derivatives to calculate stress-energy-momentum tensors is discussed in some detail. The relation of this result to tensors proposed by Abraham and others is discussed in the concluding section where the relevance of the whole approach to experiments on matter in non-inertial environments with variable gravitational and electromagnetic fields is stressed.

Physical Review A

Nonmagnetic and spherically symmetric dielectric material media are investigated in their generality as analog models, in the domains of geometrical optics, for a few relevant static and spherically symmetric solutions of gravitation, including black holes and wormholes. Typical and desirable gravitational features are systematically linked to the nonlinear properties of the phenomenological dielectric permittivity of the medium. From this, the limitations of such analogies are explored in terms of their corresponding geometric flexibility, dielectric configurations, and causal structure.

Cornell University - arXiv, 2022

In this paper, we turn our attention to light propagation in three-dimensional electrodynamics. More specifically, we investigate the behavior of light rays in a continuous bi-dimensional hypothetical medium living in a three-dimensional ambient spacetime. Relying on a fully covariant approach, we assume that the medium is endowed with a local and linear response tensor which maps field strengths into excitations. In the geometric optics limit, we then obtain the corresponding Fresnel equation and, using well known results from algebraic geometry, we derive the effective optical metric. I.

Physical Review D, 2001

We show that the propagation of photons in a nonlinear dielectric medium can be described in terms of a modification of the metric structure of space-time. We solve completely the case in which the dielectric constant ⑀ is an arbitrary function of the electric field ⑀(E). The particular case of no dependence on the field reduces to the Gordon metric.