Analogue gravity from electrodynamics in nonlinear media (original) (raw)
Analog gravity from electrodynamics in non-linear media
2000
Working with electrodynamics in the geometrical optics approximation we derive the expression representing an eectively curved geometry which guides the propagation of electromagnetic waves in material media whose physical properties depend on an external electric eld. The issue of birefringence is addressed, and the trajectory of the extraordinary ray is explicitly worked out. Quite general curves are obtained for the
Some Aspects of Electromagnetic Waves Propagating in Nonlinear Media taking Gravity into account
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.
Maxwell’s Electrodynamics in Curved Space-Time
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.
The propagation of electromagnetic waves in a gravitational field
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.
Geometrical aspects of light propagation in nonlinear electrodynamics
Physical Review D, 2000
We analyze the propagation of light in the context of nonlinear electrodynamics, as it occurs in modified QED vacua. We show that the corresponding characteristic equation can be described in terms of a modification of the effective geometry of the underlying spacetime structure. We present the general form for this effective geometry and exhibit some new consequences that result from such approach.
arXiv (Cornell University), 2022
The gravitational field of an idealized plane-wave solution of the Maxwell equations can be described in closed form. After discussing this particular solution of the Einstein-Maxwell equations, the motion of neutral test particles, which are sensitive only to the gravitational background field, is analyzed. This is followed by a corresponding analysis of the dynamics of neutral fields in the particular Einstein-Maxwell background, considering scalars, Majorana spinors and abelian vector fields, respectively.
Differential geometry approach to asymmetric transmission of light
Optics Express
In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials, through a technique now known as "transformation optics". This method, however, only applies for the particular class of metamaterials known as impedance matched, that is, materials whose electric permittivity is equal to their magnetic permeability. In that case, the material may be described by a spacetime metric. In the present work we will introduce a generalization of the geometric methods of transformation optics to situations in which the material is not impedance matched. In such situation, the material-or more precisely, its constitutive tensor-will not be described by a metric only. We bring in a second tensor, with the local symmetries of the Weyl tensor, the "W-tensor". In the geometric optics approximation we show how the properties of the W-tensor are related to the asymmetric transmission of the material. We apply this feature into the design of a particularly interesting set of asymmetric materials. These materials are birefringent when light rays approach the material in a given direction, but behave just like vacuum when the rays have the opposite direction with the appropriate polarization (or, in some cases, independently of the polarization).
Geometrical Approach to Light in Inhomogeneous Media
International Journal of Modern Physics A, 2002
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only. The introduction of an appropriately chosen threedimensional metric leads to a significant simplification of the description of light propagation in an inhomogeneous medium: light rays become geodesics of the metric and the field vectors are parallel transported along the rays. The new metric is connected to the usual flat space metric diag[1,1,1] via a conformal transformation leading to new, effective values of the medium parametersε andμ withεμ = 1. The corresponding index of refraction is thus constant and so is the effective velocity of light. Space becomes effectively empty but curved. All deviations from straight-line propagation are now due to curvature. The approach is finally used for a discussion of the Riemann-Silberstein vector, an alternative, complex formulation of the electromagnetic fields. *
On the Propagation of Gravitational Fields in Matter
Journal of Mathematical Physics, 1966
A purely covariant treatment is made of those solutions of the Einstein field equations which represent pure gravitational radiation propagating in fluid and electromagnetic media. The analysis involves a discussion of the full Bianchi identities in carefully selected tetrad frames. In this way the interaction between the gravitational field and the medium is transferred to a coupling between a preferred frame for the gravitational field and one for the matter field. The gravitational radiation no longer propagates along shear-free null geodesics, as it does in vacuum, and the shear and ray curvature of the propagation vector are shown to depend directly on the properties of the medium. Some new solutions of the field equations, representing transverse gravitational waves propagating in an electromagnetic field, are exhibited and discussed in some detail. It is shown that no such solutions exist, at least in simple cases, for perfect fluids. Finally, the treatment presented here is compared with the more usual electromagnetic treatment, and it is shown why the theories require basically different approaches.