Electromagnetic quasinormal modes of D-dimensional black holes II

By using the sixth order WKB approximation we calculate for an electromagnetic field propagating in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes its quasinormal (QN) frequencies for the fundamental mode and first overtones. We study the dependence of these QN frequencies on the value of the cosmological constant and the spacetime dimension. We also compare with the results for the gravitational perturbations propagating in the same background. Moreover we compute exactly the QN frequencies of the electromagnetic field propagating in D-dimensional massless topological black hole and for the charged D-dimensional Nariai spacetime we calculate exactly the QN frequencies of the coupled electromagnetic and gravitational perturbations.     

Kinetics of interacting gravitational and electromagnetic perturbations in cosmological plasma

The system of Einstein-Maxwell equations and a kinetic equation with a model collision integral for the cosmological plasma is used to study the behavior of gravitational and electromagnetic perturbations in the radiation-dominated stage of expansion of the universe. It is shown that gravitational perturbations are capable of generating electromagnetic fields in the cosmological plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 91–96, January, 1992.     

Propagation of transverse electromagnetic waves with gravitational perturbations in an isotropic universe

The combined behavior of gravitational and electromagnetic perturbations in the radiation-dominated plasma of an isotropic universe is considered. It is shown that transverse electromagnetic waves and vector and tensor gravitational perturbations are independent of one another. The propagation of transverse electromagnetic waves during the lepton and radiation-dominated phases is determined. It is shown that the gravitational perturbations help to excite longitudinal electromagnetic fields in the radiation-dominated plasma.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–54, December, 1985.     

Probing strange stars and color superconductivity by r-mode instabilities in millisecond pulsars

An astrophysically realistic model of wave dynamics in black-hole spacetimes must involve a nonspherical background geometry with angular momentum. We consider the evolution of gravitational (and electromagnetic) perturbations in rotating Kerr spacetimes. We show that a rotating Kerr black hole becomes "bald" slower than the corresponding spherically symmetric Schwarzschild black hole. Moreover, our results turn over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal. Our results are also of importance both to the study of the no-hair conjecture and the mass-inflation scenario (stability of Cauchy horizons).     

Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson method to non-vacuum spacetimes. Then we present three large explicit classes of solutions for high-frequency gravitational waves in particular backgrounds. These involve non-expanding (plane, spherical or hyperbolical), cylindrical, and expanding (spherical) waves propagating in various universes which may contain a cosmological constant and electromagnetic field. Relations of high-frequency gravitational perturbations of these types to corresponding exact radiative spacetimes are described.     

Transverse Wave Propagation in Relativistic Two-Fluid Plasmas around Schwarzschild-de Sitter Black Hole

We investigate transverse electromagnetic waves propagating in a plasma influenced by the gravitational field of the Schwarzschild-de Sitter black hole. Applying 3+1 spacetime split we derive the relativistic two-fluid equations to take account of gravitational effects due to the event 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. We derive the dispersion relation for these waves and solve it for the wave number k numerically.     

Transverse Wave Propagation in Relativistic Two-Fluid Plasmas around Reissner–Nordström Black Hole

We investigate transverse electromagnetic waves propagating in a plasma influenced by the gravitational field of the Reissner–Nordström black hole. Applying 3+1 spacetime split we reformulate the relativistic two-fluid equations to take account of gravitational effects due to the event horizon and describe the set of simultaneous linear equations for the perturbations. Using a local approximation we investigate the one-dimensional radial propagation of Alfvén and high frequency electromagnetic waves. We derive the dispersion relation for these waves and solve it for the wave number k numerically.     

Gravitational collapse with charge and small asymmetries. II. Interacting electromagnetic and gravitational perturbations

Paper I analyzed the evolution of nonspherical scalar-field perturbations of an electrically charged, collapsing star; this paper treats coupled electromagnetic and gravitational perturbations. It employs the results of recent detailed work in which coupled perturbations were studied in a gauge-invariant manner by using the Hamiltonian (Moncrief s) approach and the Newman-Penrose formalism, and the relations between the fundamental quantities of these two methods were obtained.It is shown that scalar-field perturbations are a prototype for coupled perturbations. The collapse produces a Reissner-Nordström black hole, and the perturbations are radiated away completely. Alll-pole parts of the perturbations of the metric and the electromagnetic field decay according to power laws; in the extreme case (e ² =M ²), the interaction causes the quadrupole perturbations to die out more slowly than the dipole perturbations.     

Quasinormal Modes of the Schwarzschild Black Hole Surrounded by the Quintessence Field in Rastall Gravity

The quasinormal modes of the Schwarzschild black hole surrounded by the quintessence in Rastall gravity are studied using the sixth-order Wentzel-Kramers-Brillouin approximative approach. The effect of the Rastall parameter on the quasinormal modes of gravitational, electromagnetic and massless scalar perturbations is explored. Compared to the case of Einstein gravity, it is found that, when η < 0, the gravitational field, electromagnetic field as well as massless scalar field damp more rapidly and have larger real frequency of oscillation in Rastall gravity, while when η > 0, the gravitational field, electromagnetic field as well as massless scalar field damp more slowly and have smaller real frequency of oscillation in Rastall gravity. It is also found that the gravitational field, electromagnetic field as well as massless scalar field damp more and more slowly and the real frequency of oscillation for the gravitational perturbation, electromagnetic perturbation as well as massless scalar perturbation becomes smaller and smaller as the Rastall parameter η increases. Compared among the quasinormal frequencies of gravitational, electromagnetic and massless scalar perturbations, I find that, for fixed η, (l, n), ∈ and N_q, the oscillation damps most slowly for the gravitational perturbation, mediate for the electromagnetic perturbation and most rapidly for the massless scalar perturbation, and the real frequency of oscillation is the smallest for the gravitational perturbation, mediate for the electromagnetic perturbation and the largest for the massless scalar perturbation in Rastall gravity.     

The motion of charged test particles in general relativity

We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.     

The method of virtual quanta as a probe of the equivalence principle

We consider bremsstrahlung encounters between a test body of massm, chargee, and a large fixed massM with chargeQ. We use the method of virtual quanta, and calculate the total electromagnetic and gravitational energy radiated in such encounters. We consider both the case in which the deflection is principally electromagnetic in nature, and the case in which the deflection is principally gravitational. The results are interpreted by considering the predictions of the equivalence principle, for the behavior of the test particle,and for the behavior of the virtual quanta. As expected from the equivalence principle, the total radiation produced is larger for electromagnetic deflection than for a gravitational deflection through the same angle.Dedicated to the memory of Alfred Schild, born7 September 1921; died 24 May 1977. A good man, a great scholar, the best of friends.Research supported in part by NSF grant no. PHV76-07919 and by NATO Research grant no. 1002.     

On perturbations of solutions of the Einstein-Maxwell equations

By using the expressions for the solutions of the Einstein-Maxwell equations in terms of potentials, valid in the case where the spacetime admits a shear-free geodesic null congruence and the electromagnetic field is aligned to it, we show that a pair of complex potentials generates simultaneous perturbations of the gravitational and the electromagnetic fields. We also show that if the background electromagnetic field is null, then the pair of complex potentials is determined by a pair of coupled, linear, second-order differential equations.     

Gravity induced magnetic instability

In the presence of a gravitational field the stability of a magnetoplasma is studied against electromagnetic perturbations. We have shown that a pinching type of instability can be triggered with a sizable growth rate affecting the equilibrium configuration of the confining magnetic field. This might have a profound effect on the magnetic fields of astrophysical bodies.     

The Electromagnetic Analogue of Some Gravitational Perturbations in Cosmology

Recently attention has been drawn to the fact that perfect fluid tensor perturbations (with perturbed vorticity and acceleration vanishing) of isotropic cosmological models have a perturbed Weyl tensor with electric part satisfying a linear, homogeneous, third-order wave equation while the magnetic part satisfies a linear, homogeneous, second-order wave equation. We construct an analogous class of electromagnetic test fields in the isotropic cosmological models for which the electric vector satisfies a third-order, linear and homogeneous wave equation while the magnetic vector satisfies a second-order, linear and homogeneous wave equation. If the perfect fluid has an equation of state we give a simplified derivation of the authors' previous perturbation analysis describing gravitational waves carrying arbitrary information. We also present the analogous solutions of Maxwell's equations which contain electromagnetic waves conveying arbitrary information.     

Test of a model coupling of electromagnetic and gravitational fields by using high-frequency gravitational waves

Models of the coupling of electromagnetic and gravitational fields have been studied extensively for many years. In this paper,we consider the coupling between the Maxwell field and the Weyl tensor of the gravitational field to study how the wavevector of the electromagnetic wave is affected by a plane gravitational wave. We find that the wavevector depends upon the frequency and direction of polarization of the electromagnetic waves, the parameter that couples the Maxwell field and the Weyl tensor, and the angle between the direction of propagation of the electromagnetic wave and the coordinate axis. The results show that this coupling model can be tested by the detection of high-frequency gravitational waves.     

On the theories of the interacting perturbations of the Reissner-Nordström black hole

A complete account of the Hamiltonian approach to the coupled perturbations of the Reissner-Nordström black hole, initiated by Moncrief, is given. All Hamiltonian equations are expressed explicitly in suitable forms; the metric and electromagnetic field perturbations are found in terms of Moncrief's gauge invariant canonical variables in the Regge-Wheeler gauge. The basic (both tetrad and coordinate) gauge invariant scalars occurring in the perturbation studies based on the Newman-Penrose formalism are then related to Moncrief's variables. The strikingly simple relations obtained enable us to show that the fundamental pair of decoupled equations, derived recently within the Newman-Penrose formalism by Chandrasekhar, can be cast into gauge invariant form, and that it can be obtained from Moncrief's formalism.It is demonstrated how the fundamental equations, supplemented by another combination of the Newman — Penrose equations, generalize the Bardeen-Press equations for uncoupled electromagnetic and gravitational perturbations of the Schwarzschild black hole.The odd and the even parityl=1 perturbations are also considered in detail. In the Appendix the relations to Zerilli's work on coupled perturbations of the Reissner-Nordström black hole are given.     

Stability of hot Reissner-Nordstrom black hole

The stability of de Sitter space in the presence of a black hole is shown. The gravitational and electromagnetic perturbations of a Reissner-Nordstrom black hole which is asymptotically de Sitter instead of asymptotically flat are considered in terms of complex potentials. This result on stability can also be applied to the inflationary scenario.     

Cosmology with inhomogeneous magnetic fields

We review spacetime dynamics in the presence of large-scale electromagnetic fields and then consider the effects of the magnetic component on perturbations to a spatially homogeneous and isotropic universe. Using covariant techniques, we refine and extend earlier work and provide the magnetohydrodynamic equations that describe inhomogeneous magnetic cosmologies in full general relativity. Specialising this system to perturbed Friedmann–Robertson–Walker models, we examine the effects of the field on the expansion dynamics and on the growth of density inhomogeneities, including non-adiabatic modes. We look at scalar perturbations and obtain analytic solutions for their linear evolution in the radiation, dust and inflationary eras. In the dust case we also calculate the magnetic analogue of the Jeans length. We then consider the evolution of vector perturbations and find that the magnetic presence generally reduces the decay rate of these distortions. Finally, we examine the implications of magnetic fields for the evolution of cosmological gravitational waves.     

Binding in Charged Spherically Symmetric Objects

We consider the subject of self-binding in static, spherically symmetric objects consisting of a charged fluid. We have shown previously that in the case of a perfect fluid, only the localized part of the mass contributes to gravitational self-binding of such objects and that in the limiting case of objects comprised purely of electromagnetic mass, there is no gravitational binding. Here, we extend this result to the more general case of an anisotropic fluid. Our inspection of the Oppenheimer–Volkov equation allows tracking of both gravitational and non-gravitational contributions to binding of spherically symmetric objects and shows that those with pure electromagnetic mass cannot exist.