scholarly journals T -model field equations: The general solution

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Joan Josep Ferrando ◽  
Salvador Mengual
Keyword(s):  
General Solution ◽  
Field Equations ◽  
Model Field

On a symbolic algebra for Hencky-Prandtl nets

1983 ◽  
Vol 94 (2) ◽  
pp. 341-350
Author(s):  
R. Hill
Keyword(s):  
General Solution ◽  
Boundary Value Problems ◽  
Classical Theory ◽  
Systematic Approach ◽  
Standard Technique ◽  
Field Equations ◽  
Infinite Matrices ◽  
Symbolic Algebra ◽  
Series Representations ◽  
Plane Deformations

AbstractIn the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.

scholarly journals Wormholes in Wyman's solution

2014 ◽  
Vol 23 (11) ◽  
pp. 1450086 ◽  
Author(s):  
J. B. Formiga ◽  
T. S. Almeida
Keyword(s):  
Scalar Field ◽  
General Solution ◽  
Detailed Analysis ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Human Beings ◽  
Einstein Field Equations ◽  
Field Equations

The most general solution of the Einstein field equations coupled with a massless scalar field is known as Wyman's solution. This solution is also present in the Brans–Dicke theory and, due to its importance, it has been studied in detail by many authors. However, this solutions has not been studied from the perspective of a possible wormhole. In this paper, we perform a detailed analysis of this issue. It turns out that there is a wormhole. Although we prove that the so-called throat cannot be traversed by human beings, it can be traversed by particles and bodies that can last long enough.

Slow stationary sources

2021 ◽  
pp. 56-64
Author(s):  
Andrew M. Steane
Keyword(s):  
General Solution ◽  
Speed Of Light ◽  
Field Equations ◽  
Vector Potentials ◽  
Linearized Theory ◽  
Stationary Sources ◽  
Metric Perturbation

The linearized theory is applied to sources such as ordinary stars whose speed is small compared to the speed of light. This yields the “gravitoelectromagnetic” theory. The gravitoelectromagnetic field equations are obtained, along with their general solution via scalar and vector potentials. It is shown how to calculate the metric perturbation, and hence the field, due to a rotating ring or a ball, and thus how to calculate orbits, timing, and the Lense-Thirring precession.

scholarly journals A note on de Sitter type solutions of Einstein's field equations

1967 ◽  
Vol 7 (4) ◽  
pp. 429-432
Author(s):  
A. H. Klotz
Keyword(s):  
General Solution ◽  
De Sitter ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations

A method of deriving a class of solutions of Einstein's field equations with symmetry of de Sitter type is investigated, and the most general solution of this kind is derived.

The general axially symmetric static solution of Einstein’s vacuum field equations

1982 ◽  
Vol 382 (1783) ◽  
pp. 467-470 ◽  
Keyword(s):  
General Solution ◽  
Potential Function ◽  
Line Element ◽  
Static Solution ◽  
Vacuum Field ◽  
Axially Symmetric ◽  
Field Equations ◽  
Axis Of Symmetry ◽  
Axisymmetric Solutions ◽  
Associated Function

The general solution in closed form, including all the static axisymmetric solutions of Weyl, is presented in the canonical coordinates ρ and z of his line element. This general solution is constructed from an arbitrary function f ( z ), which coincides with his potential function along the axis of symmetry. To illustrate how the solution may be used, a particular function f , one resulting from a Newtonian solution, is used to find both the potential function and its associated function in the line element.

scholarly journals Solution with Axial Symmetry of Einstein's Equations of Teleparallelism

1932 ◽  
Vol 3 (1) ◽  
pp. 37-45 ◽  
Author(s):  
J. D. Parsons
Keyword(s):  
Field Theory ◽  
General Solution ◽  
Axial Symmetry ◽  
Unified Field Theory ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Unified Field ◽  
Theory Of Gravitation

In a recent paper Dr G. C. McVittie discussed the solution with axial symmetry of Einstein's new field-equations in his Unified Field Theory of Gravitation and Electricity. Owing to an error in his calculation of the field equations, Dr McVittie did not obtain the general solution, which we discuss in the present paper.

scholarly journals Nonstatic Spherically Symmetric Isotropic Solutions for a Perfect Fluid in General Relativity

1978 ◽  
Vol 31 (1) ◽  
pp. 111 ◽  
Author(s):  
Max Wyman
Keyword(s):  
Differential Equation ◽  
General Relativity ◽  
General Solution ◽  
Present Author ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Perfect Fluids ◽  
Specific Choice ◽  
Total Differential

The present author (Wyman 1946) showed that all perfect fluids which can be represented by nonstatic, spherically symmetric, isotropic solutions of the Einstein field equations can be found by solving a nonlinear total differential equation of the second order involving. an arbitrary function 'P(r). Since then several particular solutions of this equation have been found. Although the four solutions given recently by Chakravarty et at. (1976) involve particular choices of 'P(r), none of these is the general solution of the equation that results from the specific choice of 'P(r) that was made. The present paper shows how these four general solutions are obtained.

scholarly journals Behaviour of the Kramer Radiating Star

1997 ◽  
Vol 50 (5) ◽  
pp. 959 ◽  
Author(s):  
S. D. Maharaj ◽  
M. Govender
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Nonlinear Differential Equation ◽  
Special Functions ◽  
Second Order ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Exterior Solution ◽  
Order Nonlinear Differential Equation ◽  
Radiating Star

We study the behaviour of the model for a radiating star proposed by Kramer. The evolution of the model is governed by a second order nonlinear differential equation. The general solution of this equation is expressed in terms of elementary and special functions. This completes the solution of the Einstein field equations for the interior of the star. The model matches smoothly to the Vaidya exterior solution and the condition p = qB is satisfied at the boundary. We briefly study the thermodynamics of the model and indicate the difficulty in specifying the temperature explicitly.

Tilted Kantowski–Sachs cosmological model in Brans–Dicke theory of gravitation

2018 ◽  
Vol 33 (04) ◽  
pp. 1850011 ◽  
Author(s):  
D. D. Pawar ◽  
S. P. Shahare ◽  
V. J. Dagwal
Keyword(s):  
General Solution ◽  
Cosmological Model ◽  
Perfect Fluid ◽  
Power Law ◽  
Tensor Field ◽  
Geometrical Parameters ◽  
Field Equations ◽  
Theory Of Gravitation

Tilted Kantowski–Sachs cosmological model in Brans–Dicke theory for perfect fluid has been investigated. The general solution of field equations in Brans–Dicke theory for the combined scalar and tensor field are obtained by using power law relation. Also, some physical and geometrical parameters are obtained and discussed.

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