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We present for the first time the nonlinear dynamics of quantum electrodynamic (QED) photon splitting in a strongly magnetized electron-positron (pair) plasma. By using a QED corrected Maxwell equation, we derive a set of equations that exhibit nonlinear couplings between electromagnetic (EM) waves due to nonlinear plasma currents and QED polarization and magnetization effects. Numerical analyses of our coupled nonlinear EM wave equations reveal the possibility of a more efficient decay channel, as well as new features of energy exchange among the three EM modes that are nonlinearly interacting in magnetized pair plasmas. Possible applications of our investigation to astrophysical settings, such as magnetars, are pointed out., Comment: 5 pages, 3 figures, to appear in Physical Review Letters

Starting from the non-relativistic Pauli description of spin-1/2 particles, a set of fluid equations, governing the dynamics of such particles interacting with external fields and other particles, is derived. The equations describe electrons, positrons, holes, and similar conglomerates. In the case of electrons, the magnetohydrodynamic limit of an electron-ion plasma is investigated. The results should be of interest and relevance both to laboratory and astrophysical plasmas., Comment: 11 pages, minor typos corrected, to appear in New Journal of Physics

The fully nonlinear governing equations for spin 1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies of the combined collective and spin dynamics. The linear response of the quantum plasma in an electron--ion system is obtained and analyzed. Applications of the theory to solid state and astrophysical systems as well as dusty plasmas are pointed out., Comment: 4 pages, 2 figures, to appear in Physical Review Letters

The modulational instability of nonlinearly interacting spatially incoherent Stokes waves is analyzed. Starting from a pair of nonlinear Schroedinger equations, we derive a coupled set of wave-kinetic equations by using the Wigner transform technique. It is shown that the partial coherence of the interacting waves induces novel effects on the dynamics of crossing sea states., Comment: 10 pages, 8 figures, to appear in JETP Letters

The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A comparison between coherent and random phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultra-short optical pulses. In practical terms, this could be achieved by using random phase plate techniques., Comment: 9 pages, 3 figures, to appear in Phys. Rev. E

Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings., Comment: 15 pages, to appear in Physics of Plasmas

In this paper we consider photon-photon scattering due to self-induced gravitational perturbations on a Minkowski background. We focus on four-wave interaction between plane waves with weakly space and time dependent amplitudes, since interaction involving a fewer number of waves is excluded by energy-momentum conservation. The Einstein-Maxwell system is solved perturbatively to third order in the field amplitudes and the coupling coefficients are found for arbitrary polarizations in the center of mass system. Comparisons with calculations based on quantum field theoretical methods are made, and the small discrepances are explained., Comment: 5 pages, 3 figures

A kinetic theory for radiation interacting with sound waves in an ultrarelativistic electron-positron plasma is developed. It is shown that the effect of a spatial spectral broadening of the electromagnetic pulse is to introduce a reduction of the growth rates for the decay and modulational instabilities. Such spectral broadening could be due to a finite pulse coherence length, or through the use of random phase filters, and would stabilize the propagation of electromagnetic pulses., Comment: 8 pages, 4 figures, to appear in Phys. Plasmas

A kinetic theory for electromagnetic ion waves in a cold relativistic plasma is derived. The kinetic equation for the broadband electromagnetic ion waves is coupled to the slow density response via an acoustic equation driven by ponderomotive force like term linear in the electromagnetic field amplitude. The modulational instability growth rate is derived for an arbitrary spectrum of waves. The monochromatic and random phase cases are studied., Comment: 7 pages, 4 figures, to appear in Physics of Plasmas

The statistical properties of the Salerno model is investigated. In particular, a comparison between the coherent and partially coherent wave modes is made for the case of a random phased wave packet. It is found that the random phased induced spectral broadening gives rise to damping of instabilities, but also a broadening of the instability region in quasi-particle momentum space. The results can be of significance for condensation of magnetic moment bosons in deep optical lattices., Comment: 3 pages, 2 figure, to appear in Physical Review A

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large amplitude freak waves in deep water., Comment: 4 pages, 4 figures, to appear in Physical Review Letters

A kinetic equation describing the nonlinear evolution of intense electromagnetic pulses in electron-positron (e-p) plasmas is presented. The modulational instability is analyzed for a relativistically intense partially coherent pulse, and it is found that the modulational instability is inhibited by the spectral pulse broadening. A numerical study for the one-dimensional kinetic photon equation is presented. Computer simulations reveal a Fermi-Pasta-Ulam-like recurrence phenomena for localized broadband pulses. The results should be of importance in understanding the nonlinear propagation of broadband intense electromagnetic pulses in e-p plasmas in laser-plasma systems as well as in astrophysical plasma settings., Comment: 16 pages, 5 figures, to appear in Phys. Plasmas

A new process associated with the nonlinear optical properties of the electromagnetic vacuum, as predicted by quantum electrodynamics, is described. This can be called photon acceleration in vacuum, and corresponds to the frequency shift that takes place when a given test photon interacts with an intense beam of background radiation., Comment: 10 pages, 2 figures, version to appear in Phys. Lett. A

The effect of short wavelength quantum electrodynamic (QED) correction on plasma-wave propagation is investigated. The effect on plasma oscillations and on electromagnetic waves in an unmagnetized as well as a magnetized plasma is investigated. The effects of the short wavelength QED corrections are most significant for plasma oscillations and for extraordinary modes. In particular, the QED correction allow plasma oscillations to propagate, and the extra-ordinary mode looses its stop band. The significance of our results is discussed., Comment: 12 pages, 5 figures

We derive expressions for the coupling coefficients for electromagnetic four-wave mixing in the non-linear quantum vacuum. An experimental setup for detection of elastic photon-photon scattering is suggested, where three incoming laser pulses collide and generate a fourth wave with a new frequency and direction of propagation. An expression for the number of scattered photons is derived and, using beam parameters for the Astra Gemini system at the Rutherford Appleton Laboratory, it is found that the signal can reach detectable levels. Problems with shot-to-shot reproducibility are reviewed, and the magnitude of the noise arising from competing scattering processes is estimated. It is found that detection of elastic photon-photon scattering may for the first time be achieved., Comment: 11 pages, 6 figures, to appear in Physical Review A

We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations., Comment: 18 pages, 8 figures

We present an investigation of the modulational instability of partially coherent signals in electrical transmission lines. Starting from the modified Ginzburg-Landau equations and the Wigner-Moyal representation, we derive a nonlinear dispersion relation for the modulational instability. It is found that the effect of signal broadbandness reduces the growth rate of the modulational instability., Comment: 5 pages, 1 figure, to appear in Physical Review E

The existence of two new low-frequency electrostatic modes in quantum dusty plasmas is pointed out. These modes can be useful to diagnose charged dust impurities in micro-electro-mechanical systems., Comment: 5 pages, to appear in Europhys. Lett

The collective production of electron-positron pairs by electrostatic waves in quantum plasmas is investigated. In particular, a semi-classical governing set of equation for a self-consistent treatment of pair creation by the Schwinger mechanism in a quantum plasma is derived., Comment: 4 pages, 3 figures, to appear in JETP Letters

The filamentational instability of spatially broadband femtosecond optical pulses in air is investigated by means of a kinetic wave equation for spatially incoherent photons. An explicit expression for the spatial amplification rate is derived and analyzed. It is found that the spatial spectral broadening of the pulse can lead to stabilization of the filamentation instability. Thus, optical smoothing techniques could optimize current applications of ultra-short laser pulses, such as atmospheric remote sensing., Comment: 8 pages, 2 figures, to appear in Optics Letters

We consider strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems. Current state-of-the-art laser facilities are close to reaching energy scales at which quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. Here we describe the implications of collective interactions between photons and photon-plasma systems. We give an overview of strong field vacuum effects and a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation-plasma is derived. Effects introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are discussed., Comment: 47 pages, accepted for publication in Rev. Mod. Phys

Nonlinear oscillations within a plasma slab are analyzed. Two types of solutions are found, depending on the initial value of the electron density. The first represents regular oscillations within the plasma slab, while the second gives rise to explosive growth at the slab centre or at the edges. The results are discussed., Comment: 5 pages, 4 figures, to appear in Journal of Plasma Physics

We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation for the pulses, making it possible to analyze and describe partial coherence in metamaterials. It is shown that a novel short pulse soliton, which is found analytically, can propagate in the medium., Comment: 6 pages, 2 figures, to appear in Phys. Rev. E

The properties of amplitude modulated broadband Alfven waves is investigated. In particular, the dynamics of circularly polarized dispersive Alfven waves, governed by a derivative nonlinear Schroedinger equation, is analyzed using the Wigner formalism. The modulational instability of random phase dispersive pump Alfven waves is investigated, and it is shown that the spectral broadening gives rise to a new mode structure., Comment: 9 pages, 2 figures, to appear in Phys. Lett. A

Photon-photon scattering, due to photons interacting with virtual electron-positron pairs, is an intriguing deviation from classical electromagnetism predicted by quantum electrodynamics (QED). Apart from being of fundamental interest in itself, collisions between photons are believed to be of importance in the vicinity of magnetars, in the present generation intense lasers, and in intense laser-plasma/matter interactions; the latter recreating astrophysical conditions in the laboratory. We show that an intense photon pulse propagating through a radiation gas can self-focus, and under certain circumstances collapse. This is due to the response of the radiation background, creating a potential well in which the pulse gets trapped, giving rise to photonic solitary structures. When the radiation gas intensity has reached its peak values, the gas releases part of its energy into `photon wedges', similar to Cherenkov radiation. The results should be of importance for the present generation of intense lasers and for the understanding of localized gamma ray bursts in astrophysical environments. They could furthermore test the predictions of QED, and give means to create ultra-intense photonic pulses., Comment: 4 pages, 1 figure

The equations governing the interaction between incoherent light and electron-acoustic waves are presented. The modulational instability properties of the system are studied, and the effect of partially coherent light is discussed. It is shown that partial coherence of the light suppresses the modulational instability. However, short wavelength perturbations are less affected, and will therefore dominate in, e.g. pulse filamentation. The results may be of importance to space plasmas and laser-plasma systems., Comment: 8 pages, 1 figure, to appear in Phys. Plasmas

The nonlinear propagation of low-frequency circularly polarized waves in a magnetized dusty plasma is analyzed. It is found that wave steepening and shock formation can take place due to the presence of nonlinear quantum vacuum effects, thus giving rise to ultra-intense electromagnetic shocks. Moreover, it is shown that solitary wave structures are admitted even under moderate astrophysical conditions. The results may have applications to astrophysical plasmas, as well as next generation laser interactions with laboratory plasmas containing dust clusters., Comment: 8 pages, 2 figures, to appear in Europhys. Lett

The properties of four-wave interaction via the nonlinear quantum vacuum is investigated. The effect of the quantum vacuum is to generate photons with new frequencies and wave vectors, due to elastic photon-photon scattering. An expression for the number of generated photons is derived and using state-of-the-art laser data it is found that the number of photons can reach detectable levels. In particular, the prospect of using the high repetition Astra Gemini system at the Rutherford Appleton Laboratory is discussed. The problem of noise sources is reviewed, and it is found that the noise level can be reduced well below the signal level. Thus, detection of elastic photon-photon scattering may for the first time be achieved., Comment: 4 pages, 3 figures (color), to appear in Physical Review Letters

We present a statistical description of Bose-Einstein condensates with general higher order nonlinearities. In particular, we investigate the case of cubic-quintic nonlinearities, of particular interest for dilute condensates. The implication of decoherence for the stability properties of the condensate is discussed., Comment: 3 pages, no figs., to appear in Eur. Phys. J. B

A kinetic theory for quantum Langmuir waves interacting nonlinearly with quantum ion-acoustic waves is derived. The formulation allows for a statistical analysis of the quantum correction to the Zakharov system. The influence of a background random phase on the modulational instability is given. In the coherent case, the effect of the quantum correction is to reduce the growth rate. Moreover, in the classical limit, a bifurcation develops in the dispersion curves due to the presence of partial coherence. However, the combined effect of partial coherence and a quantum correction may give rise to an increased modulational instability growth rate, as compared to the classical case. The results may be of significance in dense astrophysical plasmas and laboratory laser-plasma systems., Comment: 15 pages, 13 figures, to appear in Phys. Plasmas

We present a statistical description of the propagation of short pulses in long optical fibers, taking into account the Kerr and nonlocal nonlinearities on an equal footing. We use the Wigner approach on the modified nonlinear Schroedinger equation to obtain a wave kinetic equation and a nonlinear dispersion relation. The latter exhibit that the optical pulse decoherence reduces the growth rate of the modulational instability, and thereby contribute to the nonlinear stability of the pulses in long optical fibers. It is also found that the interaction between spectral broadening and nonlocality tends to extend the instability region., Comment: 9 pages, 1 figure

The stability of colliding Bose-Einstein condensates is investigated. A set of coupled Gross-Pitaevskii equations is thus considered, and analyzed via a perturbative approach. No assumption is made on the signs (or magnitudes) of the relevant parameters like the scattering lengths and the coupling coefficients. The formalism is therefore valid for asymmetric as well as symmetric coupled condensate wave states. A new set of explicit criteria is derived and analyzed. An extended instability region, in addition to an enhanced instability growth rate is predicted for unstable two component bosons, as compared to the individual (uncoupled) state., Comment: 4 pages, 1 figure

We present exact electromagnetic solitary pulses that can be experimentally obtained within nonlinear left-handed metamaterials. The effect of pulse decoherence on the modulation instability of partially incoherent electromagnetic waves is also investigated. The results may contribute to a better understanding of nonlinear electromagnetic pulse propagation in media with negative index of refraction., Comment: 3 pages, references added and typos corrected

A new nonlinear electromagnetic wave mode in a magnetized dusty plasma is predicted. Its existence depends on the interaction of an intense circularly polarized electromagnetic wave with a dusty plasma, where quantum electrodynamical photon-photon scattering is taken into account. Specifically, we consider a dusty electron-positron-ion plasma, and show that the propagation of the new mode is admitted. It could be of significance for the physics of supernova remnants and in neutron star formation., Comment: 10 pages, 1 figure, references added, matches version to appear in Phys. Plasmas

The existence of the dust acoustic wave (DAW) in a strongly magnetized electron-positron (pair)-dust plasma is demonstrated. In the DAW, the restoring force comes from the pressure of inertialess electrons and positrons, and the dust mass provides the inertia. The waves could be of interest in astrophysical settings such as the supernovae and pulsars, as well as in cluster explosions by intense laser beams in laboratory plasmas., Comment: 6 pages, revtex4

It is well-known that a charged particle moving with constant velocity in vacuum does not radiate. In a medium the situation can be different. If the so called Cherenkov condition is satisfied, i.e. the particle velocity exceeds the phase speed in the medium, the particle will radiate. We show that a charge moving with a constant velocity in a gas of photons emits Cherenkov radiation, even in the gamma-ray regime, due to nonlinear quantum electrodynamic effects. Our result is evaluated with respect to the radiation background in the early universe, and it is argued that the effect can be significant., Comment: 4 pages, to appear in New J. Phys

We present a novel nonlinear mechanism for exciting a gravitational radiation pulse (or a gravitational wave) by dust magnetohydrodynamic (DMHD) waves in dusty astrophysical plasmas. We derive the relevant equations governing the dynamics of nonlinearly coupled DMHD waves and a gravitational wave (GW). The system of equations is used to investigate the generation of a GW by compressional Alfv\'{e}n waves in a type II supernova. The growth rate of our nonlinear process is estimated, and the results are discussed in the context of the gravitational radiation accompanying supernova explosions., Comment: 4 pages

The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of wave-kinetic equations, the so called Wigner-Moyal equations. These equations are coupled to a background radiation fluid, whose dynamics is determined by an acoustic wave equation. In the slowly varying acoustic limit, we analyse the resulting system of kinetic equations, and show that they describe instabilities, as well as Landau-like damping. The instabilities may lead to break-up and focusing of ultra-high intensity multi-beam systems, which in conjunction with the damping may result in stationary strong field structures. The results could be of relevance for the next generation of laser-plasma systems., Comment: 7 pages, uses jpp.cls, to appear in J. Plasma Phys

We present a new dispersion relation for photons that are nonlinearly interacting with a radiation gas of arbitrary intensity due to photon-photon scattering. It is found that the photon phase velocity decreases with increasing radiation intensity, it and attains a minimum value in the limit of super-intense fields. By using Hamilton's ray equations, a self-consistent kinetic theory for interacting photons is formulated. The interaction between an electromagnetic pulse and the radiation gas is shown to produce pulse self-compression and nonlinear saturation. Implications of our new results are discussed., Comment: 7 pages, 1 figure, version to appear in Europhys. Lett

A new nonlinear electromagnetic wave mode in a magnetized plasma is predicted. Its existence depends on the interaction of an intense circularly polarized electromagnetic wave with a plasma, where quantum electrodynamical photon--photon scattering is taken into account. This scattering gives rise to a new coupling between the matter and the radiation. Specifically, we consider an electron--positron plasma, and show that the propagation of the new mode is admitted. It could be of significance in pulsar magnetospheres, and result in energy transport between the pulsar poles., Comment: 8 pages, 3 figures, version to appear in Plasma Phys. Control. Fusion

We consider the conversion of gravitons and photons as a four-wave mixing process. A nonlinear coupled systems of equations involving two gravitons and two photons is obtained, and the energy exchange between the different degrees of freedom is found. The scattering amplitudes are obtained, from which a crossection for incoherent processes can be found. An analytical example is given, and applications to the early Universe are discussed., Comment: 5 pages, slightly modified as compared to v1, to appear in Class. Quantum Grav. as a Letter to the Editor

Exact nonlinear equations for magnetosonic shocklets in a uniform hot magnetoplasma are derived by using the nonlinear magnetohydrodynamic equations. Analytic as well as numerical solutions of the nonlinear equations are presented. Shock-like structures of the ion fluid velocity and magnetic field (or the plasma density) perturbations are obtained. The results may have relevance to the understanding of fast magnetosonic shocklets that have been recently observed by onboard instruments of the Cluster spacecraft at the Earth's bow shock., Comment: 11 pages, 2 figures, to appear in Phys. Plasmas

The nonlinear interaction, due to quantum electrodynamical (QED) effects, between two electromagnetic pulses and a radiation gas is investigated. It is found that the governing equations admit both modulational and filamentational instabilities. The instability growth rates are derived, and the results are discussed., Comment: 7 pages, version to appear in New J. Phys

We investigate generation of electromagnetic radiation by gravitational waves interacting with a strong magnetic field in the vicinity of a vibrating Schwarzschild black hole. Such an effect may play an important role in gamma-ray bursts and supernovae, their afterglows in particular. It may also provide an electromagnetic counterpart to gravity waves in many situations of interest, enabling easier extraction and verification of gravity wave waveforms from gravity wave detection. We set up the Einstein-Maxwell equations for the case of odd parity gravity waves impinging on a static magnetic field as a covariant and gauge-invariant system of differential equations which can be integrated as an initial value problem, or analysed in the frequency domain. We numerically investigate both of these cases. We find that the black hole ringdown process can produce substantial amounts of electromagnetic radiation from a dipolar magnetic field in the vicinity of the photon sphere., Comment: 21 pages, 4 figures; AASTeX; v3 to match version to appear in ApJ

Self-phase modulation of spherical gravitational wavepackets propagating in a flat space-time in the presence of a tenuous distribution of matter is considered. Analogies with respect to similar effects in nonlinear optics are explored. Self phase modulation of waves emitted from a single source can eventually lead to an efficient energy dilution of the gravitational wave energy over an increasingly large spectral range. An explicit criterium for the occurrence of a significant spectral energy dilution is established., Comment: 11 pages

Recently Mendonca and Cardoso [Phys. Rev. D, vol. 66, 104009 (2002)] considered nonlinear gravitational wave packets propagating in flat space-time. They concluded that the evolution equation - to third order in amplitude - takes a similar form to what arises in nonlinear optics. Based on this equation, the authors found that nonlinear gravitational waves exhibit self-phase modulation and high harmonic generation leading to frequency up-shifting and spectral energy dilution of the gravitational wave energy. In this Brief Report we point out the fact - a possibility that seems to have been overlooked by Mendonca and Cardoso - that the nonlinear terms in the evolution equation cancels and, hence, that there is no amplitude evolution of the pulse. Finally we discuss scenarios where these nonlinearities may play a role., Comment: 2 pages, to appear in Phys. Rev. D

We present a proposal for a gravitational wave detector, based on the excitation of an electromagnetic mode in a resonance cavity. The mode is excited due to the interaction between a large amplitude electromagnetic mode and a quasi-monochromatic gravitational wave. The minimum metric perturbation needed for detection is estimated to the order 7.10^(-23) using current data on superconducting niobium cavities. Using this value together with different standard models predicting the occurrence of merging neutron star or black hole binaries, the corresponding detection rate is estimated to 1-20 events per year, with a `table top' cavity of a few meters length., Comment: 8 pages, 1 figure, references added

In quantum electrodynamics, photon--photon scattering can be the result of the exchange of virtual electron--positron pairs. Effectively, this gives rise to self-interaction terms in Maxwell's equations, similar to the nonlinearities due to polarization in nonlinear optics. These self-interaction terms vanish in the limit of parallel propagating waves. However if the modes generated in bounded regions are used, there will be a non-zero total effect. We show that stationary two-dimensional light bullets can form in guiding structures, due to the balancing effect of quantum electrodynamical vacuum nonlinearities on dispersion and diffraction. These light bullets are unstable and exhibit the possibility of self-focusing collapse. The consequences of our results are also discussed., Comment: 7 pages, to appear in Phys. Lett. A

We discuss how gravitational waves could amplify seed magnetic fields to strengths capable of supporting the galactic dynamo. We consider the interaction of a weak magnetic field with gravity wave distortions in almost FRW cosmologies and find that the magnitude of the original field is amplified proportionally to the wave induced shear anisotropy and, crucially, proportionally to the square of the field's initial scale. The latter makes our mechanism particularly efficient when operating on superhorizon sized magnetic fields, like those produced during inflation. In that case, the achieved amplification can easily boost magnetic strengths, which may still lie relatively close to the galactic dynamo lower limits, well within the currently accepted range., Comment: Revised version, to appear in Phys. Lett. B

Fermat's principle and variational analysis is used to analyze the trajectories of light propagating in a radially inhomogeneous medium with a singularity in the center. It is found that the light trajectories are similar to those around a black hole, in the sense that there exists a critical radius within which the light cannot escape, but spirals into the singularity., Comment: 5 pages from tex file + 3 figures (eps files)