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.

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.

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.

scholarly journals NONUNIFORM BRANEWORLD STARS: AN EXACT SOLUTION

2009 ◽  
Vol 18 (05) ◽  
pp. 837-852 ◽  
Author(s):  
J. OVALLE
Keyword(s):  
Exact Solution ◽  
Effective Density ◽  
Interior Solution ◽  
Effective Pressure ◽  
Gravity Effect ◽  
Field Equations ◽  
Matching Conditions ◽  
Physical Behavior ◽  
Exterior Solution ◽  
Weyl Scalar

In this paper the first exact interior solution to Einstein's field equations for a static and nonuniform braneworld star with local and nonlocal bulk terms is presented. It is shown that the bulk Weyl scalar [Formula: see text] is always negative inside the stellar distribution, and in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behavior inside the distribution. Using a Reissner–Nördstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.

NUMERICAL SIMULATIONS FOR SPACE–TIME FRACTIONAL DIFFUSION EQUATIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341001 ◽  
Author(s):  
LEEVAN LING ◽  
MASAHIRO YAMAMOTO
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Time Derivative ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Long Time ◽  
Liouville Fractional Derivative ◽  
Time Fractional Diffusion Equation

We consider the solutions of a space–time fractional diffusion equation on the interval [-1, 1]. The equation is obtained from the standard diffusion equation by replacing the second-order space derivative by a Riemann–Liouville fractional derivative of order between one and two, and the first-order time derivative by a Caputo fractional derivative of order between zero and one. As the fundamental solution of this fractional equation is unknown (if exists), an eigenfunction approach is applied to obtain approximate fundamental solutions which are then used to solve the space–time fractional diffusion equation with initial and boundary values. Numerical results are presented to demonstrate the effectiveness of the proposed method in long time simulations.

scholarly journals Global monopole metric in 2 + 1 dimensions

2019 ◽  
Vol 16 (01) ◽  
pp. 1950006
Author(s):  
S. Habib Mazharimousavi ◽  
M. Halilsoy
Keyword(s):  
Exact Solution ◽  
Cosmological Constant ◽  
Electric Charge ◽  
Radial Distance ◽  
Series Solutions ◽  
Global Monopole ◽  
Negative Cosmological Constant ◽  
Consistent Manner ◽  
Positive Integers

In order to obtain the geometry of a global monopole without cosmological constant and electric charge in [Formula: see text] dimensions, we make use of the broken [Formula: see text] symmetry. In the absence of an exact solution, we determine the series solutions for both the metric and monopole functions in a consistent manner that satisfies all equations in appropriate powers. The new expansion elements are of the form [Formula: see text] for the radial distance [Formula: see text] and positive integers [Formula: see text] and [Formula: see text] constrained by [Formula: see text]. To the lowest order of expansion, we find that in analogy with the negative cosmological constant the geometry of the global monopole acts repulsively, i.e. in the absence of a cosmological constant the global monopole plays at large distances the role of a negative cosmological constant.

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 Supplier selection using different metric functions

2015 ◽  
Vol 25 (3) ◽  
pp. 413-423 ◽  
Author(s):  
S.E. Omosigho ◽  
Dickson Omorogbe
Keyword(s):  
Supplier Selection ◽  
Selection Process ◽  
Fuzzy Topsis ◽  
Ideal Solution ◽  
Order Preference ◽  
Metric Functions ◽  
Metric Function ◽  
Topsis Technique ◽  
Intuitionistic Fuzzy Topsis ◽  
Selection Of

Supplier selection is an important component of supply chain management in today?s global competitive environment. Hence, the evaluation and selection of suppliers have received considerable attention in the literature. Many attributes of suppliers, other than cost, are considered in the evaluation and selection process. Therefore, the process of evaluation and selection of suppliers is a multi-criteria decision making process. The methodology adopted to solve the supplier selection problem is intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution). Generally, TOPSIS is based on the concept of minimum distance from the positive ideal solution and maximum distance from the negative ideal solution. We examine the deficiencies of using only one metric function in TOPSIS and propose the use of spherical metric function in addition to the commonly used metric functions. For empirical supplier selection problems, more than one metric function should be used.

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

Wormhole solutions in embedding class 1 space–time

2021 ◽  
Vol 36 (02) ◽  
pp. 2150015
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Safiqul Islam
Keyword(s):  
Dimensional Space ◽  
Vacuum Solution ◽  
Energy Condition ◽  
Radial Distance ◽  
Space Time ◽  
Exotic Matter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Class 1

The present work looks for new spherically symmetric wormhole solutions of the Einstein field equations based on the well-known embedding class 1, i.e. Karmarkar condition. The embedding theorems have an interesting property that connects an [Formula: see text]-dimensional space–time to the higher-dimensional Euclidean flat space–time. The Einstein field equations yield the wormhole solution by violating the null energy condition (NEC). Here, wormholes solutions are obtained corresponding to three different redshift functions: rational, logarithm, and inverse trigonometric functions, in embedding class 1 space–time. The obtained shape function in each case satisfies the flare-out condition after the throat radius, i.e. good enough to represents wormhole structure. In cases of WH1 and WH2, the solutions violate the NEC as well as strong energy condition (SEC), i.e. here the exotic matter content exists within the wormholes and strongly sustains wormhole structures. In the case of WH3, the solution violates NEC but satisfies SEC, so for violating the NEC wormhole preserve due to the presence of exotic matter. Moreover, WH1 and WH2 are asymptotically flat while WH3 is not asymptotically flat. So, indeed, WH3 cutoff after some radial distance [Formula: see text], the Schwarzschild radius, and match to the external vacuum solution.

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