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.     

Can Dilaton Fields in Astrophysical Objects be Detected?

We analyze a new class of static exact solutions of Einstein-Maxwell-Dilaton gravity with arbitrary scalar coupling constant , representing a gravitational body endowed with electromagnetic dipole moment. This class possesses mass, dipole and scalar charge parameters. A discussion of the geodesic motion shows that the scalar field interaction is so weak that it cannot be measured in gravitational fields like the sun, but it could perhaps be detected in gravitational fields like pulsars. The scalar force can be attractive or repulsive. This gives rise to the hypothesis that the magnetic field of some astrophysical objects could be fundamental.     

Breakdown of Casimir invariance in curved space‐time

It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincaré group does not satisfy the properties of Casimir invariance when applied to the non‐inertial motion of particles while in the presence of external gravitational and electromagnetic fields, where general curvilinear co‐ordinates are used to describe the momentum generators within a Fermi normal co‐ordinate framework. Specific expressions of the Casimir scalar properties are presented. While the Casimir scalar for linear momentum remains Lorentz invariant in the absence of external fields, this is no longer true for the spin Casimir scalar. Potential implications are considered for the propagation of photons, gravitons, and gravitinos as described by the spin‐3/2 Rarita‐Schwinger vector‐spinor field. In particular, it is shown that non‐inertial motion introduces a frame‐based effective mass to the spin interaction, with interesting physical consequences that are explored in detail.     

Quantized fields propagating in plane-wave spacetimes

This paper contains an account of the interaction of a quantized massive scalar field with the classicalc number gravitational field of a plane sandwich wave of arbitrary profile and polarization. It is shown that the time varying gravitational field of the wave produces no particles and the Feynman propagator for the problem is calculated exactly. This is used to show that any reasonable regularization of the vacuum expectation value of the energy momentum tensor of the field must vanish. This means that a gravitational wave far from its source will propagate without hindrance by quantum effects.     

Higgs-field gravity

It is shown that any excited Higgs field mediates an attractive scalar gravitational interaction of Yukawa type between the elementary particles, which become massive by the ground state of the Higgs field.     

Gravity induced particle production in earth’s gravitational field in TeV region

We discuss the production of particles via interaction with the earth’s gravitational field. Explicit calculations are done for high energy scalars passing through earth’s gravitational field. We show for example, that the width for the scalar processφ→3φ can become comparable with a typical weak decay width at an energy scale of a few TeV. (Similar conclusions can be drawn about particles that ultimately couple to some scalar field.) We speculate that similar processes may be responsible for many of the anomalies in the 10–10⁴ TeV experimental data.     

Radiation from relativistic particles in nongeodesic motion in a strong gravitational field

The scalar and electromagnetic radiation emitted by relativistic particles moving along the stable nongeodesic trajectories in the Kerr gravitational field are described. Two particular models of the nongeodesic motion are developed involving a slightly charged rotating black hole and a rotating black hole immersed in an external magnetic field.     

Solutions of scalar and electromagnetic wave equations in the metric of gravitational and electromagnetic waves

The wave equation for a scalar field ? and vector potentialA* are solved in the background metric of a gravitational wave. The corresponding solutions when the metric is generated by a plane electromagnetic wave, is obtained from these solutions. The solution for the scalar wave is discussed in detail. It is found that because of the interaction, two new waves are generated in the lower order approximations. One of them has the same phase dependence as the original wave while the other shows a transient character. There is no interaction when the waves are along the same direction.     

Quantum gravitational effects in an isotropic Universe with torsion

In the framework of the quasiclassical self-consistent approach we consider a nonminimally coupled scalar field which serves as a source of torsion in an isotropic homogeneous Universe. We obtain a local asymptotic expansion for the propagator of the scalar field and the effective action, taking into account the effects of vacuum polarization and interaction of scalar particles with the self-consistent gravitational field. The leading polarization contributions can be represented in general-covariant form. A simplified cosmological model is constructed which takes into account the interaction.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 5–9, September, 1988.     

Self-gravitating wave fields in a Gödel space

The properties of self-gravitating wave fields with integral spin (scalar and vector), compatible with a Gödel type space, are investigated. The simultaneous systems of Einstein's gravitational field equations and the equations corresponding to wave fields in Gödel's metric are solved. For the scalar field, the solutions are obtained for different types of interaction Lagrangians for the gravitational and scalar fields. It is shown that for a massive vector field the relations obtained between the constants lead, within the scope of the strong gravitation theory, to the classical expression for the spin of elementary particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 59–63, October, 1981.The authors are grateful to the participants of the theoretical seminar conducted by D. Ivanenko for discussing the results of this work.     

Higgs-field gravity within the standard model

Within the framework of the Glashow-Salam-Weinberg model it is shown that the Higgs field mediates an attractive scalar gravitational interaction of Yukawa type between the elementary particles which become massive by the ground state of the Higgs field after symmetry breaking.     

Constraints on unified theories from the experimental tests of the equivalence principle

The predictions of a general unified theory for the gravitational, electromagnetic and scalar field are compared with the results of the experimental tests of the equivalence principle. It is shown that the theoretical predictions do not disagree with experimental data provided that the coupling of the scalar to the electromagnetic field is suppressed by a factork 10^–3, or, alternatively, the scalar field is massive; in this case, a lower limit for its mass is obtained.     

A coupled theory of electromagnetism and gravitation

A coupling electromagnetism with a previously developed scalar theory of gravitation is presented. The principle features of this coupling are: (1) a slight alteration to the Maxwell equations, (2) the motion of a charged particle satisfies an equation with the Lorentz force-appearing on the right side in place of zero, and (3) the energy density of the electromagnetic field appears in the gravitational field equation in a manner similar to the mass term in the Klein-Gordonequation. The field of a static, spherically symmetric charged particle is computed. The electromagnetic field gives rise to l/r ² terms in the gravitational potential.     

Spinor fields in Bianchi type-I universe

A system of minimally coupled nonlinear spinor and scalar fields within the scope of a Bianchi type-I (BI) cosmological model in the presence of a perfect fluid and a cosmological constant (Λ term) is studied, and solutions to the corresponding field equations are obtained. The problem of initial singularity and the asymptotical isotropization process of the Universe are thoroughly studied. The effect of the Λ term on the character of evolution is analyzed. It is shown that some special choice of spinor field nonlinearity generates a regular solution, but the absence of singularity results in violating the dominant energy condition in the Hawking-Penrose theorem. It is also shown that a positive Λ, which denotes an additional gravitational force in our case, gives rise to an oscillatory or a non-periodic mode of expansion of the Universe depending on the choice of problem parameter. The regular oscillatory mode of expansion violets the dominant energy condition if the spinor field nonlinearity occurs as a result of self-action, whereas, in the case of a linear spinor field or nonlinear one that occurs due to interaction with a scalar field, the dominant condition remains unbroken. A system with time-varying gravitational (G) and cosmological (Λ) constants is also studied to some extent. The introduction of magneto-fluid in the system generates nonhomogeneity in the energy-momentum tensor and can be exactly solved only under some additional condition. Though in this case, we indeed deal with all four known fields, i.e., spinor, scalar, electromagnetic, and gravitational, the over-all picture of evolution remains unchanged.     

New Effect for Detecting Gravitational Waves by Amplification with Electromagnetic Radiation

The perturbation of Dirac particles moving in a constant magnetic field is calculated for simultaneously incident parallel monochromatic circular polarized electromagnetic and gravitational waves. Resonances are found which depend on the initial energy of the charged particles, the magnetic field, and the frequencies of the incident waves. A suited choice of these parameters allows the selection of only one resonance that is proportional to the product of the squares of the amplitudes of both waves. This effect is valid for all bound systems of Dirac particles interacting simultaneously with electromagnetic and gravitational waves. At least in principle this resonance effect can be used to detect the gravitational waves in the lab. For regions of the universe with strong electromagnetic and gravitational waves and suited magnetic fields this effect may play another important part for the acceleration of charged particles.     

Elementary particles as higher-dimensional tachyons

Elementary particles are described as higher-dimensional tachyonic modes. Their electromagnetic inertial mass would not match the gravitational mass unless their scalar hypercharge vanishes. The corresponding unified geometry surrounding an elementary electric monopole is extracted. Remarkably, the ingoing five-dimensional geodetic lines, associated with like-sign charged test particles, cannot classically penetrate the finite three-dimensional spherical core on which the extra-dimensional circle shrinks to a point.     

Brans-dicke plane symmetric vacuum

The general solution of the mass zero scalar field coupled to the gravitational field with the assumption of plane symmetry is exhibited and partially interpreted. Energy transfer from a gravitational wave to test particles is studied invariantly.     

On Born approximation in black hole scattering

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner–Nordström and Reissner–Nordström–de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.     

Phenomenon of gravitational repulsion in the general theory of relativity

Einstein's generalization of Newton's theory of gravitation in the general theory of relativity led not only to small quantitative differences between gravitational effects in the relativistic theory and the Newtonian theory, but also to essentially new phenomena and effects peculiar to the relativistic theory and absent in the Newtonian theory. This difference is so large that the gravitational interaction in Einstein's theory even altered the attraction-only property, characteristic of Newton's theory, the law of universal gravitation, and became both attractive and repulsive. It is notable that the nature of the repulsion in gravitational interaction already appears in the simplest case of a spherically symmetric isolated body. Einstein's equations admit for a spherical body a solution whose physical interpretation uniquely indicates the repulsive nature of a gravitational field inside the body, if the number of particles that make up the body is sufficiently large. The structure of such a body, density distribution of the number of particles, mass, and pressure, is determined in the equilibrium state by the pressure of the substance, the gravitational attraction of peripheral layers toward the center, and the gravitational repulsion of inner layers of matter away from the center. As a result of the gravitational repulsion of matter away from the center inside the body there appears a cavity, free of the matter making up the body and its electromagnetic radiation. If the body is cold, then the volume of the world tube of the cavity can differ from zero. In the opposite case, the world tube of the cavity reduces to the world line of the center, which is inaccessible to particles of matter and to electromagnetic radiation. Gravitational repulsion, on the other hand, is a result of the existence of a field singularity at the center of the body, whose world line is time-like.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 61–67, April, 1981.     

Superluminal,advanced and retarded propagation of electromagnetic potentials in quantum mechanics

In some gauges part of the classical electromagnetic potentials can propagate faster than the speed of light. In other gauges part of the electromagnetic potentials can be advanced, even though the electromagnetic field is retarded. If the conventional interaction between electromagnetic radiation and quantum mechanical charged particles, which involves the vector and scalar potentials, is used, an atom has a nonzero probability of being excited before the electromagnetic field arrives. If part of the potentials are advanced, the atom could even be excited before the sources are turned on. These spurious effects, which are gauge dependent and violate energy conservation, relativity, and causality, are due to use the conventional (gauge-dependent) interaction. When the interaction of the electromagnetic radiation and matter is treated in a manifestly gauge-invariant way, the atom is not excited before the electromagnetic field arrives, regardless of which gauge is used.