Ideal fluid with the equation of state ε=p in the field of a plane gravitational wave

An exact solution of the equations of relativistic hydrodynamics is obtained for a semiinfinite ideal fluid with the equation of state =p in the field of a plane gravitational wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 99–102, November, 1982.     

Ideal fluid with short-range scalar interactions in the field of a plane gravitational wave

An exact solution of the self-consistent equations of relativistic hydrodynamics and the scalar field equation is obtained. The solution describes motion of a fluid with short-range scalar interactions in the field of a plane gravitational wave.     

Causal Viscous Cosmological Models With Variable G and Λ

Einstein's equations with variable gravitational and cosmological constants are considered in the presence of a bulk viscous fluid source described by the truncated causal theory of Israel–Stewart, for the spatially flat homogeneous and isotropic universe. A solution is found in which the cosmological term varies inversely with the square of time. However, the gravitational constant G is found to be increasing with time.     

Possible gravitational radiation detection using the geometric phase of a light beam

An effect of geometrical phase shift is predicted for a light beam propagating in the field of a gravitational wave. For the beam travelling orthogonally to the direction of propagation of the gravitational wave from an observer and returning back after being reflected, this phase is shown to grow proportionally toL/ whereL is the distance between the observer and reflecting system, and the characteristic wavelength of the gravitational wave packet (for light propagating parallel or antiparallel to the gravitational wave, the geometric phase shift is absent). Gravitational radiation detection experiments are proposed using this new effect, the corresponding estimates being given.On leave of absence from: Peoples' Friendship University, Moscow, RussiaOn leave of absence from: Krasnoyarsk State University, Krasnoyarsk, Russia     

Abelian model of gravitating magnetic monopole

A self-consistentU(1)-gauge model in gravitational field is investigated. The exact solutions of two types of corresponding field equations are obtained. These solutions can be interpreted as magnetic monopoles. The first solution is regular forr 0 and provides an everywhere regular geometry, the second one has a physical singularity. In order to guarantee the stability of the monopoles we introduce the notion of a gravitational topological charge using de Rham's cohomology theory. This topological charge describes the sizes and the inner structure of the monopole.     

Ernst potentials for vacuum Bianchi models

We derive Ernst potentials for vacuum Bianchi I through VII models. A scheme to find inhomogeneous generalizations of such models by using generating techniques which incorporate electromagnetic fields or gravitational wave perturbations to a seed Bianchi solution is presented.On leave of absence from: Departamento de Fisica, CINVESTAV del IPN, Mexico     

On the Reconstruction of the Scalar Mode of GW170817 in Scalar-Tensor Gravity Theory

In general metric theory of gravity, a gravitational wave is allowed to have up to six polarizations: two scalar and two vector modes in addition to tensor modes. In case the number of laser-interferometric gravitational wave telescopes is larger than the number of polarizations of a gravitational wave, all the polarizations can be individually reconstructed. Since it depends on theories of gravity which polarizations the gravitational waves have, the investigation of polarizations is important for the test of theories of gravity. In order to test the scalar–tensor gravity theory, one of important alternative theories of gravity, the scalar mode of GW170817 observed by LIGO Livingstone, Hanford and Virgo is reconstructed without prior information about any tensor–scalar gravity theories. The upper limit of the scalar mode in term of the band-limited root-sum-square of the amplitude is $$ with the time window of 2 [s] and frequency window of ≈60–120 [Hz]. It is also studied how much the tensor modes are leaked into the reconstructed scalar mode, and it is found that the reconstructed scalar mode contains roughly 30% of energy leaked from the tensor modes.     

Point massive particle in General Relativity

It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle. Nevertheless, what is the exact solution of Einstein’s equations with $\delta $ δ -type source corresponding to a point particle is not known. In the present paper, we prove that the Schwarzschild solution in isotropic coordinates is the asymptotically flat static spherically symmetric solution of Einstein’s equations with $\delta $ δ -type energy-momentum tensor corresponding to a point particle. Solution of Einstein’s equations is understood in the generalized sense after integration with a test function. Metric components are locally integrable functions for which nonlinear Einstein’s equations are mathematically defined. The Schwarzschild solution in isotropic coordinates is locally isometric to the Schwarzschild solution in Schwarzschild coordinates but differs essentially globally. It is topologically trivial neglecting the world line of a point particle. Gravity attraction at large distances is replaced by repulsion at the particle neighborhood.     

Gravitational Fields and Nonlinear σ-Models

It is shown that different types of gravitational fields can be analyzed as nonlinear -models. We show that the Einstein—Hilbert action for stationary aximmetric fields, Einstein—Rosen gravitational wave, and Gowdy cosmological models can be expressed in terms of a Lagrangian density for the SL(2, R)/SO(2) -model. We discuss the possibility of using these results to quantize gravitational fields.     

Using gravitational lenses to detect gravitational waves

Gravitational lenses could be used to detect gravitational waves, because a gravitational wave affects the travel-time of a light ray. In a gravitational lens, this effect produces time-delays between the different images. Thus the bending of light, which was the first experimental confirmation of Einstein's theory, can be used to search for gravitational waves, which are the most poorly confirmed aspect of that same theory. Applying this method to the gravitational lens 0957+561 gives new upper bounds on the amplitude of low-frequency gravitational waves in the universe, and new limits on the energy-density during an early inflationary phase.This Essay received the First Award from the Gravity Research Foundation, 1990-Ed.     

On gravitational conductors,waveguides, and circuits

We show that a material with sufficiently large elastic shear modulus or shear viscosity will act like a gravitational conductor or metal. It will reflect gravitational waves, and it can be used to make gravitational waveguides and circuits. Unlike electromagnetism, a gravitational wave can be guided by a single conductor in transverse mode. Gravitational conductors can obey the dominant energy condition, and they can be larger than their Schwarzschild radius, but they must violate a new condition that is probably satisfied by all existing forms of matter. Direct-current gravitational circuits, although limits of guided gravitational waves, have a simple Newtonian interpretation.This essay is a slightly expanded version of one that received an honorable mention (1978) from the Gravity Research Foundation-Ed.Work supported in part by NSF grant No. PHY78-09616.     

Application of types-N and -O spaces to examples of exact solutions of the gravitational equations

Analysis of the exact solutions of the gravitational equations corresponding to the collision of two gravitational plane waves (typeN) and light-like beams (typeO) and also a Kerr-Schild wave metric with conformally flat background is used to formulate theorems that indicate the resulting type of spacetime if the initial gravitational fields belong to typesN andO. A type-D Weyl matrix always appears, which is due to the nonlinear super-position of gravitational fields, in contrast to the superposition of weak gravitational fields, when the sum of the Weyl matrices for the initial fields corresponds to dropping nonlinear terms in both the curvature tensor and the field equations.Work performed under the auspices of the Russian State Scientific-Technical Program Astronomiya.Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–82, May, 1995.     

A conformal mapping and isothermal perfect fluid model

Instead of the metric conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as minimally curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base spacetime can be written in the Kerr-Schild form in spherical polar coordinates. The conformal metric then admits the unique three-parameter family of perfect fluid solutions which are static and inhomogeneous. The density and pressure fall off in the curvature radial coordinates asR ^–2, for unbounded cosmological model with a barotropic equation of state. This is the characteristic of an isothermal fluid. We thus have an ansatz for an isothermal perfect fluid model. The solution can also represent bounded fluid spheres.     

The Phase of a Quantum Mechanical Particle in Curved Spacetime

We investigate the quantum mechanical wave equations for free particles of spin 0, 1/2, 1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is S/ = p dx /, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple manageable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has exactly the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in . We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in . For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.     

A Brief Guide to Variations in Teleparallel Gauge Theories of Gravity and the Kaniel-Itin Model

Recently Kaniel and Itin proposed a gravitational model with the wave type equation as vacuum field equation, where denotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corresponding mistakes in the literature. Then we turn to a detailed discussion of the Kaniel-Itin model.     

The Quantum Measurement Problem and the Possible Role of the Gravitational Field

The quantum measurement problem and various unsuccessful attempts to resolve it are reviewed. A suggestion by Diosi and Penrose for the half-life of the quantum superposition of two Newtonian gravitational fields is generalized to an arbitrary quantum superposition of relativistic, but weak, gravitational fields. The nature of the collapse process of the wave function is examined.     

Vaidya's spherically symmetric radiating solution

Conclusions An analysis of Vaidya's solution has shown that it cannot describe electromagnetic radiation in a gravitational field: the Einstein-Maxwell equations for this solution are incompatible.The neutrino treatment of this solution is somewhat dubious.An investigation using the Rodichev energy tensor and Petrov's classification indicates that there is also no gravitational radiation in this solution.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 130–132, November, 1971.In conclusion the authors wish to thank V. I. Rodichev for valuable discussions of this work.     

Gravitational Waves in Matter

The theory of gravitational waves in matter is given. This covers the questions of constitutive relation, number of independent polarizations, index of refraction, reflection and refraction at an interface, etc. The theory parallels the familiar optics of electromagnetic waves in material media, but there are some striking differences. The use of the Campbell-Morgan formalism in which the gauge-invariant tidal force dyads E and B rather than the gauge-dependent metric perturbations are the unknowns is essential. The main justification of the theory at the moment is as a theoretical exercise worth doing. The assumption: size L of the medium gravitational wave length (infinite medium) rules out application to the already well-understood detection problem, but there may be an application to gravitational wave propagation through molecular gas clouds of galactic or inter-galactic size.     

Embedding of Particle Waves in a Schwarzschild Metric Background

The special and general relativity theories are used to demonstrate that the velocity of an unradiative particle in a Schwarzschild metric background, and in an electrostatic field, is the group velocity of a wave that we call a particle wave, which is a monochromatic solution of a standard equation of wave motion and possesses the following properties. It generalizes the de Broglie wave. The rays of a particle wave are the possible particle trajectories, and the motion equation of a particle can be obtained from the ray equation. The standing particle wave equation generalizes the Schrödinger equation of wave amplitudes. The particle wave motion equation generalizes the Klein–Gordon equation; this result enables us to analyze the essence of the particle wave frequency. The equation of the eikonal of a particle wave generalizes the Hamilton–Jacobi equation; this result enables us to deduce the general expression for the linear momentum. The Heisenberg uncertainty relation expresses the diffraction of the particle wave, and the uncertainty relation connecting the particle instant of presence and energy results from the fact that the group velocity of the particle wave is the particle velocity. A single classical particle may be considered as constituted of geometrical particle wave; reciprocally, a geometrical particle wave may be considered as constituted of classical particles. The expression for a particle wave and the motion equation of the particle wave remain valid when the particle mass is zero. In that case, the particle is a photon, the particle wave is a component a classical electromagnetic wave that is embedded in a Schwarzschild metric background, and the motion equation of the wave particle is the motion equation of an electromagnetic wave in a Schwarzschild metric background. It follows that a particle wave possesses the same physical reality as a classical electromagnetic wave. This last result and the fact that the particle velocity is the group velocity of its wave are in accordance with the opinions of de Broglie and of Schrödinger. We extend these results to the particle subjected to any static field of forces in any gravitational metric background. Therefore we have achieved a synthesis of undulatory mechanics, classical electromagnetism, and gravitation for the case where the field of forces and the gravitational metric background are static, and this synthesis is based only on special and general relativity.