On the collision of impulsive gravitational waves when coupled with fluid motions

1985 ◽  
Vol 402 (1822) ◽  
pp. 37-65 ◽  
Keyword(s):  
Exact Solution ◽  
Gravitational Waves ◽  
Massive Particle ◽  
Natural Generalization ◽  
Space Time ◽  
Direct Result ◽  
Sound Waves ◽  
Time Singularity ◽  
Consistent Extension ◽  
Ultimate Result

An exact solution of Einstein’s equations, with a source derived from a perfect fluid in which the energy density, ε , is equal to the pressure, p , is obtained. The solution describes the space–time following the collision of plane impulsive gravitational waves and is the natural generalization of the Nutku─Halil solution of the vacuum equations, in the region of interaction under similar basic conditions. A consistent extension of the solution, prior to the instant of collision, requires that the fluid in the region of interaction is the direct result of a transformation of incident null-dust (i. e. of massless particles describing null trajectories). The ultimate result of the collision is the development of a space─time singularity, the nature of which is strongly dependent on the amplitude and the character of the sound waves that are present. The distribution of ε that follows the collision has many intriguing features. The solution obtained in this paper provides the first example of an induced transformation of a massless into a massive particle.

On the dispersion of cylindrical impulsive gravitational waves

1987 ◽  
Vol 412 (1842) ◽  
pp. 75-91 ◽  
Keyword(s):  
Exact Solution ◽  
Wave Packet ◽  
Gravitational Waves ◽  
Time Derivative ◽  
Radial Distance ◽  
Space Time ◽  
Principal Feature ◽  
Metric Functions ◽  
Metric Function ◽  
Weyl Scalar

An exact solution, describing the dispersion of a wave packet of gravita­tional radiation, having initially (at time t = 0) an impulsive character, is analysed. The impulsive character of the wave-packet derives from the space-time being flat, except at a radial distance ϖ = ϖ 1 (say) at t = 0, and the time-derivative of the Weyl scalars exhibiting δ-function singu­larities at ϖ = ϖ 1 , when t → 0. The principal feature of the dispersion is the development of a singularity of the metric function, v , and of the Weyl scalar, ψ 2 , when the wave, after reflection at the centre, collides with the still incoming waves. The evolution of the metric functions and of the Weyl scalars, as the dispersion progresses, is illustrated graphically.

Some exact solutions of gravitational waves coupled with fluid motions

1985 ◽  
Vol 402 (1823) ◽  
pp. 205-224 ◽  
Keyword(s):  
Exact Solutions ◽  
Gravitational Waves ◽  
Perfect Fluid ◽  
Space Time ◽  
Velocity Of Sound ◽  
Time Singularity ◽  
Einstein's Equations ◽  
The Past ◽  
Velocity Of Light ◽  
Cosmological Solutions

Some exact solutions of Einstein’s equations are found which represent the interaction of gravitational waves with a perfect fluid in which the velocity of sound equals the velocity of light. These solutions, unlike the solutions representing the collision of impulsive gravitational waves, are bounded by a space–time singularity and have some resemblance to cosmological solutions: every time-like trajectory, extended into the past, encounters the singularity. Moreover, in the generic case, matter may be considered as being created at the singularity.

scholarly journals Janis–Newman–Winicour and Wyman Solutions are the Same

1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Total Energy ◽  
Space Time ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Equations

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

A Linear Acoustic Phased Array for Nonreciprocal Transmission and Reception

2020 ◽  
Author(s):  
R. Adlakha ◽  
M. Moghaddaszadeh ◽  
M. A. Attarzadeh ◽  
A. Aref ◽  
M. Nouh
Keyword(s):  
Phase Modulation ◽  
Frequency Conversion ◽  
Phased Array ◽  
Space Time ◽  
Mathematical Framework ◽  
Sound Waves ◽  
Asymmetric Transmission ◽  
Time Modulation ◽  
Dynamic Phase ◽  
Phase Angles

Abstract Acoustic phased arrays are capable of steering and focusing a beam of sound via selective coordination of the spatial distribution of phase angles between multiple sound emitters. Here, we propose a controllable acoustic phased array with space-time modulation that breaks time-reversal symmetry, and enables phononic transition in both momentum and energy spaces. By leveraging the dynamic phase modulation, the proposed linear phased array is no longer bound by the reciprocity principle, and supports asymmetric transmission and reception patterns that can be tuned independently. Through theoretical and numerical investigations, we develop and verify a mathematical framework to characterize the nonreciprocal phenomena, and analyze the frequency conversion between the wave fields. The space-time acoustic phased array facilitates unprecedented control over sound waves in a variety of applications including underwater telecommunication.

De la combinatoire du modèle de l'échiquier de Feynman et des fonctions spéciales

1984 ◽  
Vol 62 (7) ◽  
pp. 632-638
Author(s):  
J. G. Williams
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
Hypergeometric Series ◽  
Jacobi Polynomials ◽  
Dimensional Space ◽  
Space Time ◽  
Continuous Limit ◽  
Two Dimensional ◽  
Dimensional Space Time

The exact solution of the Feynman checkerboard model is given both in terms of the hypergeometric series and in terms of Jacobi polynomials. It is shown how this leads, in the continuous limit, to the Dirac equation in two-dimensional space-time.

scholarly journals Gravitational waves and the breaking of parallelograms in space-time

2013 ◽  
Vol 45 (6) ◽  
pp. 1163-1177 ◽  
Author(s):  
J. W. Maluf ◽  
S. C. Ulhoa ◽  
J. F. da Rocha-Neto
Keyword(s):  
Gravitational Waves ◽  
Space Time

The Gravity Funnels, formed by the longitudinal vortices, according to the new Axioms and Laws

2021 ◽  
Vol 4 (1) ◽  
Keyword(s):  
Gravitational Waves ◽  
Scientific Theory ◽  
Transverse Direction ◽  
Modern Science ◽  
Longitudinal Direction ◽  
Space Time ◽  
The Other ◽  
Longitudinal Vortices ◽  
New Space ◽  
The One

In the age of information, it is no secret that the modern science is in a very difficult position. On the one hand, it has high hopes for solving the problems of modern humanity and very practical tasks. On the other hand, science shows limited potential and difficulty in carrying out the tasks. Beyond scientific theory remain such phenomena as gravity and gravitational waves and other unexplored and very useful phenomena. Obviously, the reason for these limited capabilities of modern science is its limited foundation. The foundation of science is determined by its basic axioms. If we expand the foundation of science, we will be able to build a more comprehensive, perfect and voluminous theory. In two monographs and a series of articles the author offers a system of extended axioms (with two new axioms) and a more extended theory (with eight new laws). To the great surprise of even the author, this new theory turned out to be extensive enough to cover and explain and the gravity. Moreover, the extended axioms and theory directly and naturally outlined the algorithm in the explanation of the so-called Gravity Funnels. According to the new axioms and laws, Gravity Funnels are both for suction (accelerating) and for expansion (decelerating). Expansion Gravity Funnel decelerates along its longitudinal direction as emits the matter in the transverse direction. In this way it consumes energy and generates matter. Suction Gravity Funnel accelerates along its longitudinal direction as sucks the matter in transverse direction. In this way it consumes matter and generates energy. The both of Funnels are situated in a new Space-time. The Space-time of decelerating and accelerating Funnels is packed by longitudinal vortices, in which the Space (S) is constant. It is radically different of the Space-Time where we live now. The Space-time where we live now is packed by cross vortices, where the time (T) is constant. According the new Axioms and Laws the two described Space- times are mutually orthogonal.

Generalization of Gravitation Theory

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Empty Space ◽  
Mathematical Structure ◽  
Physical Reality ◽  
Natural Generalization ◽  
Theory Of Relativity ◽  
Total Field ◽  
Principle Of Equivalence ◽  
Field Equations ◽  
Starting Point ◽  
Consistent Extension

This chapter attempts to formulate a consistent extension of the theory of general relativity. The starting point of the general theory of relativity is the recognition of the unity of gravitation and inertia (principle of equivalence). From this principle, it follows that the properties of “empty space” were to be represented by a symmetrical tensor expressed in the theory. The principle of equivalence, however, does not give any clue as to what may be the more comprehensive mathematical structure on which to base the treatment of the total field comprising the entire physical reality. As such, this chapter considers the problem of how to find a field structure which is a natural generalization of the symmetrical tensor as well as a system of field equations for this structure which represent a natural generalization of certain equations of pure gravitation.

scholarly journals Relativistic Reference Frames of Local Observer and Space Radiointerferometer

1990 ◽  
Vol 141 ◽  
pp. 115-117
Author(s):  
A.N. Alexandrov ◽  
S.L. Parnovsky ◽  
V.I. Zhdanov
Keyword(s):  
Light Source ◽  
Reference Frames ◽  
Natural Generalization ◽  
Space Time ◽  
Coordinate Representation ◽  
Fermi Coordinates ◽  
Local Observer

In a considerable number of works on relativistic astrometry (see, e.g. Kovalevsky and Brumberg 1986) the reference frames (RFs) are introduced either by means of coordinate representation of a space-time metric, such as using harmonicity conditions (Brumberg and Kopejkin 1989), or on the basis of invariant constructions like Fermi coordinates (Synge 1960; Ashby and Bertotti 1986; Boucher 1986). Both approaches must, probably, be combined in applications. We consider the local observer RFs (LORFs) based on the Fermi coordinates and on the optical ones (Synge 1960), which are rigorously defined for a general metric and are directly related to observable quantities. In particular, the optical RF operates with the observed direction of the light source, whereas the Fermi RF seems to be a natural generalization of the classical Cartesian RF.

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