Self-Interacting Gas in a Gravitational Wave Field

We investigate a relativistic self-interacting gas in the field of an external pp gravitational wave. Based on symmetry considerations we ask for those forces which are able to compensate the imprint of the gravitational wave on the macroscopic 4-acceleration of the gaseous fluid. We establish an exactly solvable toy model according to which the stationary states which characterize such a situation have negative entropy production and are accompanied by instabilities of the microscopic particle motion. These features are similar to those which one encounters in phenomena of self-organization in many-particle systems.     

Shock wave driven out by a piston in a mixture of a non-ideal gas and small solid particles under the influence of the gravitation field with monochromatic radiation

Similarity solutions for a spherical shock wave in a mixture of small solid particles of micro size and a non-ideal gas are discussed under the influence of the gravitational field with monochromatic radiation. The solid particles are uniformly distributed in the mixture, and the shock wave is assumed to be driven by a piston. It is assumed that the equilibrium flow-conditions are maintained and the moving piston continuously supplies the variable energy input. Due to the central mass ($\overline{m}$) at the origin (Roche model), the medium is considered to be under the influence of the gravitational field. In comparison to the attraction of the central mass at the origin, the gravitational effect of the mixture itself is neglected. The density of the undisturbed medium is assumed to be constant in order to obtain the self-similar solutions. The effect of the parameter of non-idealness of the gas $\overline{b}$, the mass concentration of solid particles in the mixture μ_p, the ratio of the density of solid particles to the initial density of the gas G_a and the gravitational parameter G₀ are obtained. It is shown that due to an increase in the gravitational parameter the compressibility of the medium at any point in the flow field behind the shock front decrease and the flow variables velocity, pressure, radiation flux and shock strength are increased. Also, an increase in the ratio of the density of solid particles to the initial density of the gas G_a and the gravitational parameter G₀ has the same effect on the shock strength and the reverse effect on the compressibility. The non-idealness of the gas causes a decrease in the shock strength and widens the disturbed region between the piston and the shock.     

Gravitational-wave background as an initiator of longitudinal structure formation in a confined relativistic gas

Exactly integrable models of a confined relativistic gas in the field of a high-intensity gravitational wave are investigated. It is shown that the development of irreversible phenomena and structure formation under the action of modulation of boundary conditions form the principal element of the effect of gravitational waves on physical systems.V. I. Ul'yanov-Lenin University, Kazan'. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 73–78, June, 1992.     

Confinement of charged particles by an electromagnetic wave leaving the region of a strong gravitational field

The interaction of a charged particle in vacuum with a circularly polarized wave leaving the region of a strong static gravitational field in the direction of a magnetostatic field is considered. It turns out that this combination of fields forms, generally speaking, two capture regions (CR₁ and CR₂) on the phase cylinder of the particle. The evolution of these regions is determined by the gravitational field. The influence of the gravitational field on the rigidity of confinement of the particle in one of these regions (CR₁) is investigated. It is shown that the rigidity of confinement of particles with relatively high energies may increase toward the periphery of the gravitational field. The possibility of particle escape by the wave is demonstrated for particles whose initial energy is insufficient to leave the gravitational field region in the absence of the wave. In this case, the particle is trapped by the wave in CR₁ and subsequently confined. The mechanism of trapping the particle is discussed. Taganrog State Radio-Engineering University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–10, June, 2000.     

Accurate solution of the boundary problem for collisionless gas in the field of a plane gravitational wave

An accurate solution of the Cauchy problem is found for a general-relativity collisionless kinetic equation against the background of the metric of a nonlinear plane gravitational field with an arbitrary law of gas-particle reflection from a boundary of any specified form. It is shown that in the field of a gravitational wave, interaction of the gas with the boundary necessarily leads to the appearance of shock waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 41–45, December, 1985.It remains to thank the participants of the gravitation seminar at Kazan' State University for discussions of the work.     

Resonance photons in a gravitational radiation field and the regularization problem for the energy-momentum tensor

The exact solutions of the relativistic kinetic equation for a photon gas subjected to the influence of a relativistic fluid and a gravitational radiation field are analyzed. Singular solutions describing resonance and entrained photons moving at a gravitational wave front are investigated. The problem of the divergence of the energy-momentum tensor in models admitting resonance photons is discussed.V. I. Ul'yanov (Lenin) State University, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 70–75, October, 1994.     

The exact behavior of electromagnetic Faraday rotation in crossing a gravitational sandwich wave in general relativity

We have analyzed the exact behavior of the polarization vector of a linearly polarized electromagnetic shock wave upon crossing a gravitational sandwich wave, by using Einstein's theory of general relativity. The Faraday rotation in the polarization vector of the electromagnetic field is induced in this nonlinear process. We show that the Faraday's angle highly depends on the electromagnetic parameter, gravitational parameter and the width of the gravitational sandwich wave.     

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.     

Self-Similar Solution of Spherical Shock Wave Propagation in a Mixture of a Gas and Small Solid Particles with Increasing Energy under the Influence of Gravitational Field and Monochromatic Radiation

Similarity solution for a spherical shock wave with or without gravitational field in a dusty gas is studied under the action of monochromatic radiation. It is supposed that dusty gas be a mixture of perfect gas and micro solid particles. Equilibrium flow condition is supposed to be maintained and energy is varying which is continuously supplied by inner expanding surface. It is found that similarity solution exists under the constant initial density. The comparison between the solutions obtained in gravitating and non-gravitating medium is done. It is found that the shock strength increases with an increase in gravitational parameter or ratio of the density of solid particles to the initial density of the gas, whereas an increase in the radiation parameter has decaying effect on the shock waves.     

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.     

Gravitational Faraday Effect Produced by a Ring Laser

Using the linearized Einstein gravitational field equations and the Maxwell field equations it is shown that the plane of polarization of an electromagnetic wave is rotated by the gravitational field created by the electromagnetic radiation of a ring laser. It is further shown that this gravitational Faraday effect shares many of the properties of the standard electromagnetic Faraday effect. An experimental arrangement is then suggested for the observation of this gravitational Faraday effect induced by the ring laser.     

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.     

Relativistic gas in a gravitational field

Equations describing the kinetics and hydrodynamics of a relativistic gas in a gravitational field are obtained using the concept of a gravitational field as a physical field in a pseudo-Euclidean space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 17–20, September, 1982.     

Pair production by gravitational waves in the field of a black hole

We consider the production of scalar particles by a gravitational wave incident on the static gravitational field of a Schwarzschild mini black hole.     

Evaluation and preliminary measurement of the interaction of a dynamical gravitational near field with a cryogenic gravitational wave antenna

We present a detailed analysis of the effect of the gravitational field generated by a small rotating quadrupole on a graviational wave antenna and we report on the preliminary measurement of this effect on the Explorer 2270 kg cryogenic gravitational wave antenna of the Rome group. The induced signal had an amplitude twenty times larger than the detector noise when the antenna was equipped with an FET amplifier and was easily detected without requiring integration in time. We remark that with this method we were able to make an absolute calibration of a gravitational wave antenna.     

Colliding Plane Waves in Einstein–Maxwell Theory

Recently, a simple solution of the vacuum Einstein–Maxwell field equations was given describing a plane electromagnetic shock wave sharing its wave front with a plane gravitational impulse wave. We present here an exact solution of the vacuum Einstein–Maxwell field equations describing the head-on collision of such a wave with a plane gravitational impulse wave. The solution has the Penrose–Khan solution and a solution obtained by Griffiths as separate limiting cases.     

A new type of quantum interferometer for gravitational wave detection

We present an orientational quantum interferometer sensitive to gravitational waves that is based on orienting quantum objects like molecules, atoms, or nuclei in space. The detection principle is based on inducing non-sphericity to the corresponding wave functions by light-pulses. In the field of a gravitational wave these objects then possess spectra that depend on their orientation in space. In our measurement scheme we investigate the adiabatic influence of a monochromatic gravitational wave over a quarter gravitational wave period and compare the corresponding frequencies at instances with maximal and vanishing gravitational wave elongation. We therefore explore the effect over a quarter gravitational wave period (or wavelength) and the resulting frequency shift scales with the binding energy of the system times the amplitude of the gravitational wave. In particular, a gravitational wave with amplitude h = 10⁻²³ will induce a frequency shift of the order of 110 μHz for an atom interferometer based on a 91-fold charged uranium ion.     

Gravitational radiation and the removal of a degeneracy with respect to hidden parameters in relativistic hydrodynamics

We consider the evolution of a viscous heat-conducting fluid, initially found in a state of local thermodynamic equilibrium, in the field of a gravitational wave. It is shown that in the process of action on the hydrodynamic system the field of the gravitational wave imposes an anisotropy and inhomogeneity characteristic of it, removing the degeneracy with respect to the transport coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 108–113, August, 1993.     

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.