The curved spacetime Maxwell equations are applied to the anisotropically expanding Kasner metrics. Using the application of vector identities we derive 2$^\textrm{nd}$-order differential wave equations for the electromagnetic field components; through this explicit derivation, we find that the 2$^\textrm{nd}$-order wave equations are not uncoupled for the various components (as previously assumed), but that gravitationally-induced coupling between the electric and magnetic field components is generated directly by the anisotropy of the expansion. The lack of such coupling terms in the wave equations from several prior studies may indicate a generally incomplete understanding of the evolution of electromagnetic energy in anisotropic cosmologies. Uncoupling the field components requires the derivation of a 4$^\textrm{th}$-order wave equation, which we obtain for Kasner-like metrics with generalized expansion/contraction rate indices. For the axisymmetric Kasner case, $(p_{1}, p_{2}, p_{3}) = (1,0,0)$, we obtain exact field solutions (for general propagation wavevectors), half of which appear not to have been found before in previous studies. For the other axisymmetric Kasner case, $\{p_{1}, p_{2}, p_{3}\} = \{(-1/3),(2/3),(2/3)\}$, we use numerical methods to demonstrate the explicit violation of the geometric optics approximation at early times, showing the physical phase velocity of the wave to be inhibited towards the initial singularity, with $v \rightarrow 0$ as $t \rightarrow 0$.
Bounded Electromagnetic Power Flux at Naked Kasner Singularities
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（阿根廷国家科学研究委员会）；Instituto Balseiro (UNCUYO)（巴尔塞罗研究所）；Universidad Diego Portales（迭戈·波特莱斯大学）；Universidad de La Serena（拉塞雷纳大学）
We consider a D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or cosmological Einstein-Maxwell vacuum spacetimes. We mainly focus on electrovacuum solutions and four different types of solutions are obtained in which one of them has no four dimensional counterpart. We also consider the properties of the general solution corresponding to the exterior field of a charged line mass and discuss its several properties. Although it resemb…
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, CAS（中国科学院新疆天文台射电天文与技术重点实验室）；College of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
The scalar wave equation in Kasner spacetime is solved, first for a particular choice of Kasner parameters, by relating the integrand in the wave packet to the Bessel functions. An alternative integral representation is also displayed, which relies upon the method of integration in the complex domain for the solution of hyperbolic equations with variable coefficients. In order to study the propagation of wave fronts, we integrate the equations of bicharacteristics which are null geodesics, and we are able to express them, for the first time in the literature, with the help of elliptic integral…
The present work investigates some exact solutions of the gravitational wave equation in some widely used cosmological spacetimes. The examples are taken from spatially flat and closed isotropic models as well as Kasner metric which is anisotropic. Various matter distributions are considered, from the standard dust or radiation distribution to exotic matters like that with an equation of state $P = - \frac{1}{3} ρ$. In almost all cases the frequency and amplitude of the wave are found to be decaying with evolution, except for a closed radiation universe where there is a resurgence of the wavef…
Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated to linear polarization) and dispersion. The particular case of a vacuum--dominated anisotropic Universe, which reproduces a Friedmann-Robertson-Walker Universe (for late times) while for earlier times it matches a Kasner Universe, is studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is now dependen…
The redshift of light is calculated for an anisotropic cosmological spacetime. Two different approaches are considered. In the first one, electromagnetic waves are modeled using the geometrical optics (high--frequency) approximation. This approach considers light rays following null geodesics, being equivalent to the motion followed by pointlike spinless massless particles. It is shown that the redshift for this case depends, in general, on the direction of propagation, and is dispersive (wavelength dependent) for light emitted from different points of an extended object. In the second approac…
We present a method developed to deal with electromagnetic wave propagation inside a material medium that reacts, in general, non-linearly to the field strength. We work in the context of Maxwell' s theory in the low frequency limit and obtain a geometrical representation of light paths for each case presented. The isotropic case and artificial birefringence caused by an external electric field are analyzed as an application of the formalism and the effective geometry associated to the wave propagation is exhibited.
The propagation of light through bianisotropic materials is studied in the geometrical optics approximation. For that purpose, we use the quartic general dispersion equation specified by the Tamm-Rubilar tensor, which is cubic in the electromagnetic response tensor of the medium. A collection of different and remarkable Fresnel (wave) surfaces is gathered, and unified via the projective geometry of Kummer surfaces.
An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton wave and strong non-soliton electromagnetic traveling wave of arbitrary profile propagating in the expanding universe (the symmetric Kasner spacetime) is presented. In contrast to intuitive expectations that rather strong traveling waves can destroy the soliton, it occurs that the soliton survives during its interaction with electromagnetic wave of arbitrary amplitude and profile, but its parameters begin to evolve under the influence of this interaction. If a traveli…
Disturbing of a spacetime geometry may result in the appearance of an oscillating and damped radiation - the so-called quasinormal modes. Their periods of oscillations and damping coefficients carry unique information about the mass and the angular momentum, that would allow one to identify the source of the gravitational field. In this talk we present recent bounds on the diffused energy, applicable to the Schwarzschild spacetime, that give also rough estimates of the energy of excited quasinormal modes.
The propagation of free electromagnetic radiation in the field of a plane gravitational wave is investigated. A solution is found one order of approximation beyond the limit of geometrical optics in both transverse--traceless (TT) gauge and Fermi Normal Coordinate (FNC) system. The results are applied to the study of polarization perturbations. Two experimental schemes are investigated in order to verify the possibility to observe these perturbations, but it is found that the effects are exceedingly small.
A pair of wave equations is presented for the gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled and determines the propagation of the electromagnetic perturbation. The other is for the propagation of the shear of a principal null direction and has a source term given by the solution of the first equation. This result is expected to have important applications in astrophysical models.
In this note we provide a simple explanation of the recent finding of anisotropy in electromagnetic (EM) propagation claimed by Nodland and Ralston (astro-ph/9704196). We consider, as a possible origin of such effect, the effective coupling between EM fields and some tiny background torsion field. The coupling is obtained after integrating out charged fermions, it is gauge invariant and does not require the introduction of any new physics.
We report on the occurrence of negative-phase-velocity (NPV) planewave propagation in the ergosphere of a rotating black hole. By implementing the Kerr metric, it is demonstrated that regions of NPV propagation are concentrated at the equator of the ergosphere, while NPV propagation is less common towards the polar regions. Increasing the angular velocity of the black hole exaggerates the NPV concentration at the equator. NPV propagation is not observed outside the stationary limit surface.
We study the electromagnetic field equations on an arbitrary quantum curved background in the semiclassical approximation of Loop Quantum Gravity. The effective interaction hamiltonian for the Maxwell and gravitational fields is obtained and the corresponding field equations, which can be expressed as a modified wave equation for the Maxwell potential, are derived. We use these results to analyze electromagnetic wave propagation on a quantum Robertson-Walker space time and show that Lorentz Invariance is not preserved. The formalism developed can be applied to the case where back reaction effe…
The behavior of massive quantum fields in the general plane wave spacetime and external, non-plane, electromagnetic waves is studied. The asymptotic conditions, the "in" ("out") states and the cross sections are analysed. It is observed that, despite of the singularities encountered, the global form of these states can be obtained: at the singular points the Dirac delta-like behavior emerges and there is a discrete change of phase of the wave function after passing through each singular point. The relations between these phase corrections and local charts are discussed. Some examples of waves …
We study the propagation of Maxwellian electromagnetic waves in curved spacetimes in terms of the appropriate geometrical optics limit, notions of signal speed, and minimal coupling prescription from Maxwellian theory in flat spacetime. In the course of this, we counter a recent major claim by Asenjo and Hojman (2017) to the effect that the geometrical optics limit is partly ill-defined in Gödel spacetime; we thereby dissolve the present tension concerning established results on wave propagation and the optical limit.
We study the electromagnetic wave propagation in the joint dilaton field and axion field. Dilaton field induces amplification/attenuation in the propagation while axion field induces polarization rotation. The amplification/attenuation induced by dilaton is independent of the frequency (energy) and the polarization of electromagnetic waves (photons). From observations, the agreement with and the precise calibration of the cosmic microwave background (CMB) to blackbody radiation constrains the fractional change of dilaton |Δψ|/ψ to less than about 8 x 10^(-4) since the time of the last scatteri…
We explicitly solve the equations for the propagation of an electromagnetic wave up to the subleading order geometric optics expansion in the Kerr spacetime. This is done in two nontrivial steps. We first construct a set of parallel propagated null tetrad in Kerr spacetime. Two of the components of such tetrad give the propagation and polarization of an electromagnetic wave in geometric optics approximation. Then we use the parallel propagated tetrad to solve the modified trajectory equation in Kerr spacetime. We obtain the wavelength-dependent deviation of the trajectory of electromagnetic wa…
The transverse electromagnetic waves propagating in a relativistic two-fluid plasma influenced by the gravitational field of the Reissner-Nordström-de Sitter black hole has been investigated exploiting 3+1 split of spacetime. Reformulating the two-fluid equations, the set of simultaneous linear equations for the perturbations have been derived. Using a local approximation, the one-dimensional radial propagation of Alfvén and high frequency electromagnetic waves are investigated. The dispersion relation for these waves is obtained and solved numerically for the wave number.
The propagation of electromagnetic plane waves with negative phase velocity (NPV) is considered in Schwarzschild-(anti-)de Sitter spacetime. It is demonstrated that NPV propagation occurs in Schwarzschild-de Sitter spacetime at lower values of the cosmological constant than is the case for de Sitter spacetime. Furthermore, we report that neither is NPV propagation observed in Schwarzschild-anti-de Sitter spacetime, nor is it possible outside the event horizon of a Schwarzschild blackhole.
We investigate the solution of Maxwell's equations in curved spacetime within the framework of Modified Gravity (MOG). We show that besides the null-geodesic treatment of photons in MOG, using Maxwell's equations and covariant coupling with the extra vector sector of gravitation in MOG, we can extract the equation for the propagation of light. We obtain Fermat's potential and calculate the deflection angle of light during lensing from a point-like star. Our results show that the deflection angle obtained from the solution of the wave equation in MOG for the large-scale structures with larger i…
Examining the propagation of electromagnetic plane waves with the wavevector directed in opposition to the time-averaged Poynting vector in cosmological spacetime with piecewise uniform metric, we show that such negative-phase-velocity (NPV) propagation is possible in certain de Sitter spacetimes but not in anti-de Sitter spacetimes. This difference suggests the possibility of an optical/electromagnetic experiment to discern the cosmological constant of a four-dimensional universe stemming from a five-dimensional brane universe.
We investigate transverse electromagnetic waves propagating in a plasma in the de Sitter space. Using the 3+1 formalism we derive the relativistic two-fluid equations to take account of the effects due to the horizon and describe the set of simultaneous linear equations for the perturbations. We use a local approximation to investigate the one-dimensional radial propagation of Alfvén and high frequency electromagnetic waves and solve the dispersion relation for these waves numerically.
Inhomogeneous Cosmologies with Bumpy Structure from Superfluid Pionic Vortices and the propagation of electromagnetic field
Centro de Estudios Científicos (CECs)（科学研究中心）；Facultad de Ingeniería, Universidad San Sebastián（塞巴斯蒂安大学工程学院）；Instituto de Ciencias Fisicas y Matemáticas, Universidad Austral de Chile（智利南方大学物理与数学科学学院）；Departamento de Ciencias Físicas, Universidad de La Frontera（弗雷兰特大学物理系）；Institute of Systems Science, Durban University of Technology（德班理工大学系统科学研究所）；Centro de Investigación, Innovación y Creación (CIIC), Universidad Católica de Temuco（特木科天主教大学创新与研究中心）；Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco（特木科天主教大学工程学院数学与物理系）；National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）
We show exact solutions of Born-Infeld theory for electromagnetic plane waves propagating in the presence of static background fields. The non-linear character of Born-Infeld equations generates an interaction between background and wave that changes the speed of propagation and adds a longitudinal component to the wave. As a consequence, in a magnetic background the ray direction differs from the propagation direction --a behavior resembling the one of a wave in an anisotropic medium--. This feature could open up a way to experimental tests of Born-Infeld theory.
