A description is made of the process of excitation of coupled longitudinal-transverse gravitational waves during the propagation of a strong electromagnetic wave in a vacuum and when a standing electromagnetic wave exists in the Fabry-Perot resonator. It is shown that such waves lead to the appearance of transverse gravitational waves in empty space. It was established that two standing high-frequency electromagnetic waves in a Fabry-Perot resonator with close frequencies cause the appearance of a low-frequency transverse gravitational wave in empty space.
We present an electromagnetic analog of gravitational wave memory. That is, we consider what change has occurred to a detector of electromagnetic radiation after the wave has passed. Rather than a distortion in the detector, as occurs in the gravitational wave case, we find a residual velocity (a "kick") to the charges in the detector. In analogy with the two types of gravitational wave memory ("ordinary" and "nonlinear") we find two types of electromagnetic kick.
The generalization of electromagnetic and gravitational hopfions is performed in terms of a complex scalar field. New definition of topological charge for linearized gravity is given. Quasi-local (super-)energy densities are compared for gravitational hopfion.
We investigate the generation of electromagnetic and gravitational radiation in the vicinity of a perturbed Schwarzschild black hole. The gravitational perturbations and the electromagnetic field are studied by solving the Teukolsky master equation with sources, which we take to be locally charged, radially infalling, matter. Our results show that, in addition to the gravitational wave generated as the matter falls into the black hole, there is also a burst of electromagnetic radiation. This electromagnetic field has a characteristic set of quasinormal frequencies, and the gravitational radiat…
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative solutions of Maxwell's vacuum field equations. The gravitational case involves a novel form of the radiative Robinson--Trautman solutions of Einstein's vacuum field equations.
We present an exact solution of the Bargmann-Michel-Telegdi (BMT) equations for the dynamics of a spin particle in external electromagnetic and gravitational pp-wave fields. We demonstrate that an anomalous magnetic moment gives rise to an additional spin rotation which is modulated both by the electromagnetic and by the gravitational wave periodicities.
A theoretical description of electromagnetic waves in the background of a (weak) gravitational wave is presented. Explicit expressions are obtained for the Stokes parameters during the passage of a plane-fronted gravitational wave described by the Ehlers-Kundt metric. In particular, it is shown that the axis of the polarization ellipse oscillates, its ellipticity remaining constant.
It is shown that, in the case of Kerr-Newman space-time, the complex electromagnetic strength E + i H and analogous complex intensity of the gravitational field share the common complexified spatial direction.
The gravitational analog of the electromagnetic Poynting vector is constructed using the field equations of general relativity in the Hilbert gauge. It is found that when the gravitational Poynting vector is applied to the solution of the linear mass quadrupole oscillator, the correct gravitational quadrupole radiation flux is obtained. Further to this, the Maxwell-like gravitational Poynting vector gives rise to Einstein's quadrupole radiation formula. The gravitational energy-momentum (pseudo) tensor obtained is symmetric and traceless. The former property allows the definition of angular mo…
Wave propagation of field disturbances is ubiquitous. The electromagnetic and gravitational are cousin theories in which the corresponding waves play a relevant role to understand several related physical. It has been established that small electromagnetic waves can generate gravitational waves and vice versa when scattered by a charged black hole. In the realm of cylindrical spacetimes, we present here a simple nonlinear effect of the conversion of electromagnetic to gravitational waves reflected by the amount of mass extracted from them.
A method is given which renders indirect detection of strong gravitational waves possible. This is based on the reflection (collision) of a linearly polarized electromagnetic shock wave from (with) a cross polarized impulsive and shock gravitational waves in accordance with the general theory of relativity. This highly non-linear process induces a detectable Faraday rotation in the polarization vector of the electromagnetic field.
We consider colliding wave packets consisting of hybrid mixtures of electromagnetic, gravitational and scalar waves. Irrespective of the scalar field, the electromagnetic wave still reflects from the gravitational wave. Some reflection processes are given for different choice of packets in which the Coulomb-like component $Ψ_2$ vanishes. Exact solution for multiple reflection of an electromagnetic wave from successive impulsive gravitational waves is obtained in a closed form. It is shown that a succesive sign flip in the Maxwell spinor arises as a result of encountering with an impulsive trai…
It is argued that static electromagnetic sources induce Weyl-Majumdar-Papapetrou solutions for the spacetime metric. The acceleration in such fields has a term many orders of magnitude stronger than usual perturbative terms. Two electrostatic and two magnetostatic examples are given.
We present the derivation and the solutions to the coupled electromagnetic and gravitational perturbations with sources in a charged black hole background. We work in the so called ghost gauge and consider as source of the perturbations the infall of radial currents. In this way, we study a system in which it is provoked a response involving both, gravitational and electromagnetic waves, which allows us to analyze the dependence between them. We solve numerically the wave equations that describe both signals, characterize the waveforms and study the relation between the input parameters of the…
We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) tha…
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.
We develop a gauge theory of the combined gravitational-electromagnetic field by expanding the Poincaré group to include clock synchronization transformations. We show that the electromagnetic field can be interpreted as a local gauge theory of the synchrony group. According to this interpretation, the electromagnetic field equations possess nonlinear terms and electromagnetic gauge transformations acquire a space-time interpretation as local synchrony transformations. The free Lagrangian for the fields leads to the usual Einstein-Maxwell field equations with additional gravitational-electroma…
The idea that the seed primordial magnetic fields can be explained by the nonminimal coupling between gravitational and electromagnetic fields is discussed. The predicted values of the magnetic field of the spiral galaxies are in agreement with the observations.
The interaction between gravitational and electromagnetic waves in the presence of a static magnetic field is studied. The field strength of the static field is allowed to surpass the Schwinger critical field, such that the quantum electrodynamical (QED) effects of vacuum polarization and magnetization are significant. Equations governing the interaction are derived and analyzed. It turns out that the energy conversion from gravitational to electromagnetic waves can be significantly altered due to the QED effects. The consequences of our results are discussed.
We present a unified investigation of memory effect in Einstein-Maxwell theory. We specify two types of memory effect, a velocity kick and a position displacement, by examining the motion of a single free falling charged test particle. Our result recovers the two known gravitational memory effect formulas and the two known electromagnetic memory effect formulas.
The quasinormal modes of the electromagnetic and gravitational perturbation on Schwarzschild-AdS black hole calculated by Cardoso and Lemos has been revisited. Although the equations of motion are correct some frequencies calculated previously by the authors are not. We present the new values of quasinormal modes and discuss the possible sources of problems and implications on the conclusions presented.
We argue that if particularly powerful electromagnetic afterglows of the gravitational waves bursts will be observed in the future, this could be used as a strong observational support for some suggested quantum alternatives for black holes (e.g., firewalls and gravastars). A universal absence of powerful afterglows should be taken as a suggestive argument against such hypothetical quantum-gravity objects.
We derive the equations for the odd and even parity perturbations of coupled electromagnetic and gravitational fields of a black hole with an electric charge within the context of general nonlinear electrodynamics. The Lagrangian density is a generic function of the Lorentz invariant scalar quantities of the electromagnetic fields. We include the Hodge dual of the electromagnetic field tensor and the cosmological constant in our calculations. For each type of parity, we reduce the system of Einstein field equations coupled to nonlinear electrodynamics to two coupled Schrödinger-type wave equat…
In this paper, we have considered how to detect the processes of plane gravitational waves colliding. The degenerate Ferrari-Ibanez solution describes the collision of plane gravitational waves with aligned linear polarization, and the solution of the interaction region is Schwarzschild-like metric by taking coordinate transformation, which impels us more interesting to detect the process to explore. We have calculated explicitly out the solutions of the electromagnetic field produced by the plane gravitational wave and the colliding region of plane gravitational waves perturbing a weak magnet…
In this paper, we discuss the effects of electromagnetic field on the dynamical instability of a spherically symmetric expansionfree gravitational collapse. Darmois junction conditions are formulated by matching interior spherically symmetric spacetime to exterior Reissner-Nordstr$\ddot{o}$m spacetime. We investigate the role of different terms in the dynamical equation at Newtonian and post Newtonian regimes by using perturbation scheme. It is concluded that instability range depends upon pressure anisotropy, radial profile of energy density and electromagnetic field, but not on the adiabatic…
We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a suitable boundary value problem. This puts on solid ground previous approximate calculations. We find consistency with previous results obtained from eikonal expansions at the level of accuracy accessible to current gravitational wave detectors.
It is still an open issue if astrophysical black holes have electric charges or not. In this work, we analytically calculate gravitational and electromagnetic waveforms in the frequency domain for charged black hole binaries during the inspiral phase. In addition to the well-known $f^{-7/6}$ waveforms, we also get a $-11/6$ power law gravitational wave component. The phase of waveforms for charged binary is fully derived. In the case of electromagnetic counterparts, we focus on the electromagnetic dipole radiation, but we include the quadrupole contribution to complete our discussion. We also …
The well known Geodesic Equation of General Relativity is newly formulated in Weyl two-spinor language in a convenient way susceptible of being combined with a set of two-spinor equations, equivalent to the Lorentz Force of Electrodynamics, obtained in previous studies. General spinor equations of motion for a test charged spin 1/2 particle in arbitrary electromagnetic and gravitational fields fields are obtained describing not only spacetime trajectories but also spin precession. For the case of the Schwarzschild metric and radial trajectories, spinor equations unifying gravitational and elec…
This is an English translation of the paper M.B.Mensky, in: K.P.Stanyukovich (ed.), "Problems of Theory of Gravity and Elementary Particles", issue 6, Moscow, Atomizdat, 1975, p.181-190 (in Russian). This paper elaborates further the idea (formulated in 1971 by Braginsky and Mensky) of detecting high-frequency gravitational waves by observing resonance action of a gravitational wave on the electromagnetic wave in a closed resonator (waveguide). The phenomenon underlying such a detector was called gravitational-electromagnetic resonance (GER). In the present paper both closed (for example circu…
Graviatom existence conditions have been found. The graviatoms (quantum systems around mini-black-holes) satisfying these conditions contain the following charged particles: the electron, muon, tau lepton, wino, pion and kaon. Electric dipole and quadrupole and gravitational radiations are calculated for the graviatoms and compared with Hawking's mini-hole radiation.
Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasi-stability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate time-averaged fields, is used to test the requirement of quasi-stability. It is found that the modified perturbation theory results in an internal inconsistency. The time-scale of evolution is found to be of the same order in magnitude as the …
We obtain all ``regularization parameters'' (RP) needed for calculating the gravitational and electromagnetic self forces for an arbitrary geodesic orbit around a Schwarzschild black hole. These RP values are required for implementing the previously introduced mode-sum method, which allows a practical calculation of the self force by summing over contributions from individual multipole modes of the particle's field. In the gravitational case, we provide here full details of the analytic method and results briefly reported in a recent Letter [Phys. Rev. Lett. {\bf 88}, 091101 (2002)]. In the el…
In previous work the authors analysed the global properties of an approximate model of radiation damping for charged particles. This work is put into context and related to the original motivation of understanding approximations used in the study of gravitational radiation damping. It is examined to what extent the results obtained previously depend on the particular model chosen. Comparisons are made with other models for gravitational and electromagnetic fields. The relation of the kinetic model for which theorems were proved to certain many-particle models with radiation damping is exhibite…
We lay a theoretical foundation in the observation of gravitational waves (GWs) by electromagnetic waves (EMWs) performing a full electromagnetic analysis without any optical approximation. For that, the perturbation of plane EMWs is obtained by solving the perturbed Maxwell equation with GWs in the Minkowski background spacetime. In a GW detector using the EMWs, we propose to measure the electromagnetic invariants that are independent of the motion of the EMW receiver and whose perturbations are gauge-invariant. Imposing a physical boundary condition at EMW emitters, we have analytic results …
The propagation of plane electromagnetic waves in the gravitational field inside a rotating cloud of dark matter is analyzed. Formulas for the deflection and absorption of light, and the rotation of the polarization plane are obtained in closed form in terms of the mass density and the angular velocity of the cloud. It is shown that the formulas can be considerably simplified for axisymmetric configurations. As an example, the formalism is applied to a rotating massive cloud described by a Plummer potential.
We discuss the relation between the gravitational and electromagnetic fields as governed by the Einstein-Maxwell field equations. It is emphasized that the tendency of the gravitational field to induce electromagnetic effects increases as the size of the system goes down. In particular, the gravitational field, according to general relativity, tends to become dominated by the spin at distances of the order of the Compton wavelength. The relevant quantity which governs this behavior is the ratio S/M^2 where S is the (spin) angular momentum. For an electron, S/M^2 ~ 10^44. Therefore, gravitomagn…
Consistency of $GL(3,R)$ gauge theory of gravity coupled with an external electromagnetic field, is studied. It is shown that possible restrictions on Maxwell field can be avoided through introduction of auxiliary fields.
We have studied the quasinormal modes and the late-time tail behaviors of scalar, electromagnetic and gravitational perturbations in the Schwarzschild black hole pierced by a cosmic string. Although the metric is locally identical to that of the Schwarzschild black hole so that the presence of the string will not imprint in the motion of test particles, we found that quasinormal modes and the late-time tails can reflect physical signatures of the cosmic string. Compared with the scalar and electromagnetic fields, the gravitational perturbation decays slower, which could be more interesting to …
This paper investigates the five-dimensional(5D) spherically symmetric gravitational collapse with positive cosmological constant in the presence of an electromagnetic field. The junction conditions between the 5D non-static interior and the static exterior spacetimes are derived using the Israel criteria modified by Santos. We use the energy conditions to discuss solution to the field equations of the interior spacetime with a charged perfect fluid for the marginally bound and the non-marginally bound cases. We found that the range of apparent horizon was larger than that for 4D gravitational…
We consider the self-force on a charged particle moving in a curved spacetime with a background electromagnetic field, extending previous studies to situations in which gravitational and electromagnetic perturbations are comparable. The formal expression $f^{ret}_α$ for the self-force on a particle, written in terms of the retarded perturbed fields, is divergent, and a renormalization is needed to find the particle's acceleration at linear order in its mass $m$ and charge $e$. We assume that, as in previous work in a Lorenz gauge, the renormalization for accelerated motion comprises an angle a…
We analyze asymptotic structure of general gravitational and electromagnetic fields near an anti-de Sitter-like conformal infinity. Dependence of the radiative component of the fields on a null direction along which the infinity is approached is obtained. The directional pattern of outgoing and ingoing radiation, which supplements standard peeling property, is determined by the algebraic (Petrov) type of the fields and also by orientation of principal null directions with respect to the timelike infinity. The dependence on the orientation is a new feature if compared to spacelike infinity.
A manifestly gauge invariant formulation of the coupling of the Maxwell theory with an Einstein Cartan geometry is given, where the space time torsion originates from a massless Kalb-Ramond field augmented by suitable U(1) Chern Simons terms.We focus on the situation where the torsion violates parity, and relate it to earlier proposals for gravitational parity violation.
Brief review of principal ideas in respect of the high frequency gravitational radiation generated and detected in the laboratory condition is presented. Interaction of electro-magnetic and gravitational waves into a strong magnetic field is considered as a more promising variant of the laboratory GW-Hertz experiment. The formulae of the direct and inverse Gertsenshtein-Zeldovich effect are derived. Numerical estimates are given and a discussion of a possibility of observation of these effects in a lab is carried out.
We study the head-on collision of linearly polarized, high frequency plane gravitational waves and their electromagnetic counterparts in the Einstein-Maxwell theory. The post-collision space-times are obtained by solving the vacuum Einstein-Maxwell field equations in the geometrical optics approximation. The head-on collisions of all possible pairs of these systems of waves is described and the results are then generalised to non-linearly polarized waves which exhibit the maximum two degrees of freedom of polarization.
We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner-Nordström geometry using the Newman Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function $Ψ_4$, as is well known, but for the electromagnetic signal the information is encoded in the function $χ$ which relates the perturbations of the radiative Maxwell scalars $φ_2$ and the Weyl scalar $Ψ_3$. In deriving the perturbation equations we do not impose any gauge condition and our analysis contains as a limiting case the …
The trajectory deflection and gravitational-electromagnetic dual lensing (GEL) of charged signal in general charged static and spherically symmetric spacetimes are considered in this work. We showed that the perturbative approach previously developed for neutral particles can be extended to the electromagnetic interaction case. The deflection angle still takes a (quasi-)series form and the finite distance effect of both the source and observer can be taken into account. Comparing to pure gravitational case, the apparent angles of the images in the GEL, their magnifications and time delay all r…
Bardeen de-Sitter (BdS) black hole is a spherically symmetric solution of Einstein's equation which is coupled to nonlinear electromagnetic field in a way that one gets a regular solution, devoid of any singularity at the origin. We compute the quasinormal (QN) frequencies for BdS black hole due to electromagnetic and gravitational perturbations. We analyse the behaviour of both real and imaginary parts of BdS QN frequencies by varying the black hole parameters and compare frequencies with Reissner-Nordström de-Sitter (RN-dS) black hole. Interestingly, we find that the response of BdS and RN-d…
The gravitational redshift forms the central part of the majority of the classical tests for the general theory of relativity. It could be successfully checked even in laboratory experiments on the earth's surface. The standard derivation of this effect is based on the distortion of the local structure of spacetime induced by large masses. The resulting gravitational time-dilation near these masses gives rise to a frequency change of any periodic process, including electromagnetic oscillations as the wave propagates across the gravitational field. This phenomenon can be tackled with classical …
We compare the nature of electromagnetic fields and of gravitational fields in linearized general relativity. We carry out this comparison both mathematically and visually. In particular the "lines of force" visualizations of electromagnetism are contrasted with the recently introduced tendex/vortex eigenline technique for visualizing gravitational fields. Specific solutions, visualizations, and comparisons are given for an oscillating point quadrupole source. Among the similarities illustrated are the quasistatic nature of the near fields, the transverse 1/r nature of the far fields, and the …
Pairs of Planck-mass-scale drops of superfluid helium coated by electrons (i.e., "Millikan oil drops"), when levitated in the presence of strong magnetic fields and at low temperatures, can be efficient quantum transducers between electromagnetic (EM) and gravitational (GR) radiation. A Hertz-like experiment, in which EM waves are converted at the source into GR waves, and then back-converted at the receiver from GR waves back into EM waves, should be practical to perform. This would open up observations of the gravity-wave analog of the Cosmic Microwave Background from the extremely early Big…
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.
We study the physical consequences of two diffferent but closely related perturbation schemes applied to the Einstein-Maxwell equations. In one case the starting space-time is flat while in the other case it is Schwarzschild. In both cases the perturbation is due to a combined electric and magnetic dipole field. We can see, within the Einstein-Maxwell equations a variety of physical consequences. They range from induced gravitational energy-momentum loss, to a well defined spin angular momentum with its loss and a center-of-mass with its equations of motion.
Superconductors will be considered as macroscopic quantum gravitational antennas and transducers, which can directly convert upon reflection a beam of quadrupolar electromagnetic radiation into gravitational radiation, and vice versa, and thus serve as practical laboratory sources and receivers of microwave and other radio-frequency gravitational waves. An estimate of the transducer conversion efficiency on the order of unity comes out of the Ginzburg-Landau theory for an extreme type II, dissipationless superconductor with minimal coupling to weak gravitational and electromagnetic radiation f…
We numerically investigate the threshold of black-hole formation in the gravitational collapse of electromagnetic waves in axisymmetry. We find approximate power-law scaling $ρ_{\rm max}\sim (η_*-η)^{-2γ}$ of the maximum density in the time evolution of near-subcritical data with $γ\simeq 0.145$, where $η$ is the amplitude of the initial data. We directly observe approximate discrete self-similarity in near-critical time evolutions with a log-scale echoing period of $Δ\simeq 0.55$. The critical solution is approximately the same for two families of initial data, providing some evidence of univ…
In this paper, the effect of electromagnetic field has been investigated on the spherically symmetric collapse with the perfect fluid in the presence of positive cosmological constant. Junction conditions between the static exterior and non-static interior spherically symmetric spacetimes are discussed. We study the apparent horizons and their physical significance. It is found that electromagnetic field reduces the bound of cosmological constant by reducing the pressure and hence collapsing process is faster as compared to the perfect fluid case. This work gives the generalization of the perf…
