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.

scholarly journals Spherically Symmetric Charged Dust Distribution in General Relativity. I. General Solution

1980 ◽  
Vol 33 (4) ◽  
pp. 765 ◽  
Author(s):  
BK Nayak
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Charge Density ◽  
Mass Density ◽  
Maxwell Field ◽  
Charged Dust ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Mathematical Condition ◽  
Dust Distribution

The Einstein-Maxwell field equations characterizing a spherically symmetric charged dust distnbution are solved exactly without imposing any mathematical condition on them. The solution is expressed in terms of two arbitrary variables and these can be chosen to correspond to an arbitrary ratio of charge density to mass density, thus allowing the possibility of understanding the interior of the horizon in a more precise manner.

ON TIME DISLOCATION SOLUTION OF EINSTEIN FIELD EQUATIONS

1999 ◽  
Vol 14 (02) ◽  
pp. 93-97 ◽  
Author(s):  
L. C. GARCIA DE ANDRADE
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
External Solution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Birkhoff Theorem ◽  
The Core ◽  
Theory Of Gravity ◽  
Gauge Theory Of Gravity

The theory considered here is not Einstein general relativity, but is a Poincaré type gauge theory of gravity, therefore the Birkhoff theorem is not applied and the external solution is not vacuum spherically symmetric and tachyons may exist outside the core defect.

scholarly journals Does general relativity highlight necessary connections in nature?

Synthese ◽  
2021 ◽  
Author(s):  
Antonio Vassallo
Keyword(s):  
General Relativity ◽  
Laws Of Nature ◽  
Coupling Mechanism ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Bianchi Identities ◽  
Physical Role ◽  
General Relativistic ◽  
Differential Relations ◽  
Necessary Connections

AbstractThe dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein’s equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities—qua part of a physical law—highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature.

scholarly journals "Gravitationally Lensed Gravitation" (GLG)

2021 ◽  
Author(s):  
Andreas Boenke
Keyword(s):  
General Relativity ◽  
Field Strength ◽  
Free Fall ◽  
Gravitational Effect ◽  
Gravitational Lens ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Optical Illusions ◽  
Spacetime Curvature ◽  
Background Object

The intention of this paper is to point out a remarkable hitherto unknown effect of General Relativity. Starting from fundamental physical principles and phenomena arising from General Relativity, it is demonstrated by a simple Gedankenexperiment that a gravitational lens enhances not only the light intensity of a background object but also its gravitational field strength by the same factor. Thus, multiple images generated by a gravitational lens are not just optical illusions, they also have a gravitational effect at the location of the observer! The "Gravitationally Lensed Gravitation" (GLG) may help to better understand the rotation curves of galaxies since it leads to an enhancement of the gravitational interactions of the stars. Furthermore, it is revealed that besides a redshift of the light of far distant objects, the cosmic expansion also causes a corresponding weakening of their gravitational effects. The explanations are presented entirely without metric representation and tensor formalism. Instead, the behavior of light is used to indicate the effect of spacetime curvature. The gravitation is described by the field strength which is identical to the free fall acceleration. The new results thus obtained provide a reference for future numerical calculations based on the Einstein field equations.

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.

The Einstein field equations

2019 ◽  
pp. 52-58
Author(s):  
Steven Carlip
Keyword(s):  
General Relativity ◽  
Conservation Laws ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Noether’S Theorem ◽  
Geodesic Deviation ◽  
Fundamental Equations ◽  
Hilbert Action ◽  
Qualitative Discussion

The Einstein field equations are the fundamental equations of general relativity. After a brief qualitative discussion of geodesic deviation and Newtonian gravity, this chapter derives the field equations from the Einstein-Hilbert action. The chapter contains a derivation of Noether’s theorem and the consequent conservation laws, and a brief discussion of generalizations of the Einstein-Hilbert action.

Approximate solutions of the general relativity field equations with a scalar meson field

1963 ◽  
Vol 59 (4) ◽  
pp. 739-741 ◽  
Author(s):  
J. Hyde
Keyword(s):  
General Relativity ◽  
Scalar Meson ◽  
Empty Space ◽  
Approximate Solutions ◽  
Spherically Symmetric ◽  
Coordinate Transformations ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Image Position ◽  
Scalar Meson Field

It was shown by Birkhoff ((1), p. 253) that every spherically symmetric solution of the field equations of general relativity for empty space,may be reduced, by suitable coordinate transformations, to the static Schwarzschild form:where m is a constant. This result is known as Birkhoff's theorem and excludes the possibility of spherically symmetric gravitational radiation. Different proofs of the theorem have been given by Eiesland(2), Tolman(3), and Bonnor ((4), p. 167).

scholarly journals Generalized Phenomenological Models of Dark Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Prasenjit Paul ◽  
Rikpratik Sengupta
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Phenomenological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Parameters ◽  
The Universe ◽  
Matter Energy

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

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