RADIATING COLLAPSE WITH VANISHING WEYL STRESSES

2005 ◽  
Vol 14 (03n04) ◽  
pp. 667-676 ◽  
Author(s):  
S. D. MAHARAJ ◽  
M. GOVENDER
Keyword(s):  
Irreversible Thermodynamics ◽  
Temperature Profiles ◽  
Junction Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Extended Irreversible Thermodynamics ◽  
Recent Approach ◽  
Dust Solution ◽  
Limiting Case

In a recent approach in modeling a radiating relativistic star undergoing gravitational collapse the role of the Weyl stresses was emphasized. It is possible to generate a model which is physically reasonable by approximately solving the junction conditions at the boundary of the star. In this paper we demonstrate that it is possible to solve the Einstein field equations and the junction conditions exactly. This exact solution contains the Friedmann dust solution as a limiting case. We briefly consider the radiative transfer within the framework of extended irreversible thermodynamics and show that relaxational effects significantly alter the temperature profiles.

scholarly journals The Gravitomagnetism in the Solar System

2017 ◽  
Vol 45 ◽  
pp. 1760052
Author(s):  
Flavia Rocha ◽  
Manuel Malheiro ◽  
Rubens Marinho
Keyword(s):  
Mass Density ◽  
Slow Motion ◽  
Weak Field ◽  
Einstein Equations ◽  
Dipole Potential ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Perihelion Advance ◽  
Motion Approximation

In 1918, Joseph Lense and Hans Thirring discovered the gravitomagnetic (GM) effect of Einstein field equations in weak field and slow motion approximation. They showed that Einstein equations in this approximation can be written as in the same form as Maxwell’s equation for electromagnetism. In these equations the charge and electric current are replaced by the mass density and the mass current. Thus, the gravitomagnetism formalism in astrophysical system is used with the mass assuming the role of the charge. In this work, we present the deduction of gravitoelectromagnetic equations and the analogue of the Lorentz force in the gravitomagnetism. We also discuss the problem of Mercury’s perihelion advance orbit, we propose solutions using GM formalism using a dipole-dipole potential for the Sun-Planet interaction.

scholarly journals ENERGY–MOMENTUM DISTRIBUTION: SOME EXAMPLES

2007 ◽  
Vol 22 (10) ◽  
pp. 1935-1951 ◽  
Author(s):  
M. SHARIF ◽  
M. AZAM
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Momentum Distribution ◽  
Special Class ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Degenerate Solution ◽  
Dust Solution

In this paper, we elaborate the problem of energy–momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for four exact solutions of the Einstein field equations. We take the gravitational waves, special class of Ferrari–Ibanez degenerate solution, Senovilla–Vera dust solution and Wainwright–Marshman solution. It turns out that these prescriptions do provide consistent results for special class of Ferrari–Ibanez degenerate solution and Wainwright–Marshman solution but inconsistent results for gravitational waves and Senovilla–Vera dust solution.

NULL SURFACES AND CONTACT GEOMETRY

2005 ◽  
Vol 02 (02) ◽  
pp. 481-496
Author(s):  
S. FRITTELLI ◽  
N. KAMRAN ◽  
C. KOZAMEH ◽  
E. T. NEWMAN
Keyword(s):  
General Relativity ◽  
Contact Geometry ◽  
Lorentzian Geometry ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Differential Systems ◽  
Exterior Differential Systems ◽  
Exterior Differential ◽  
Recent Approach ◽  
Null Surfaces

We give a self-contained and geometric account of a recent approach to the Einstein field equations of general relativity, based on families of null foliations of space–time. We then use exterior differential systems to make explicit the correspondence between conformal Lorentzian geometry in dimensions three and four and the contact geometry of special classes of differential systems.

Some special solutions in Bianchi type VI0 cosmological models with modified chaplygin gas in general relativity

2015 ◽  
Vol 24 (02) ◽  
pp. 1550017 ◽  
Author(s):  
S. D. Katore ◽  
S. P. Hatkar ◽  
S. N. Bayaskar
Keyword(s):  
Cold Dark Matter ◽  
Bianchi Type ◽  
Complete Solution ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Modified Model ◽  
Geometrical Properties

In the present paper, the role of modified chaplygin gas models in relation with the Bianchi type VI0 universe is examined. For obtaining complete solution of Einstein field equations, it is assumed that expansion scalar in the model is proportional to shear scalar and equation of state of this modified model is valid from the radiation era to the Lambda cold dark matter (ΛCDM) model. State finder and various physical, geometrical properties have also been discussed.

scholarly journals Charged anisotropic spherical collapse with heat flow

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Kali Charan ◽  
Om Prakash Yadav ◽  
B. C. Tewari
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Junction Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Radiating Star ◽  
Large Round ◽  
High Degree

AbstractIn this article, we study the shear-free gravitational collapse of a charged radiating star. The Einstein field equations of gravitational collapse for the charged stars are known to give rise to a high degree of non-linearity in the ordinary differential equation coming from junction conditions. The attempts to solve it analytically proved to be unfortunate. Numerical methods have been suggested in the past. However, the high degree of non-linearity tends to introduce fluctuations and large round off errors in the numerical calculation. A new ansatz is proposed in the present work to reduce the degree of non-linearity. An ordinary differential equation is derived by satisfying junction conditions, and its numerical solution is demonstrated. Physical quantities associated with the collapse process are plotted to observe the effect of charge on these quantities. It is concluded that the charge can delay the collapse of a star and can even prevent it depending upon the amount of charge. It is also verified that the solution satisfies all the energy conditions.

Cartesian Fingerprints in Beckett's Imagination Dead Imagine

2012 ◽  
Vol 21 (2) ◽  
pp. 223-243
Author(s):  
Irit Degani-Raz
Keyword(s):  
The Self ◽  
Levels Of Abstraction ◽  
The Media ◽  
The Mind ◽  
Limiting Case

The idea that Beckett investigates in his works the limits of the media he uses has been widely discussed. In this article I examine the fiction Imagination Dead Imagine as a limiting case in Beckett's exploration of limits at large and the limits of the media he uses in particular. Imagination Dead Imagine is shown to be the self-reflexive act of an artist who imaginatively explores the limits of that ultimate medium – the artist's imagination itself. My central aim is to show that various types of structural homologies (at several levels of abstraction) can be discerned between this poetic exploration of the limits of imagination and Cartesian thought. The homologies indicated here transcend what might be termed as ‘Cartesian typical topics’ (such as the mind-body dualism, the cogito, rationalism versus empiricism, etc.). The most important homologies that are indicated here are those existing between the role of imagination in Descartes' thought - an issue that until only a few decades ago was quite neglected, even by Cartesian scholars - and Beckett's perception of imagination. I suggest the use of these homologies as a tool for tracing possible sources of inspiration for Beckett's Imagination Dead Imagine.

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 Mass-radius relation of compact objects

2019 ◽  
Vol 15 (S356) ◽  
pp. 383-384
Author(s):  
Seman Abaraya ◽  
Tolu Biressa
Keyword(s):  
Numerical Analysis ◽  
Equation Of State ◽  
Compact Objects ◽  
Mass Limit ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Formation And Evolution ◽  
Active Research ◽  
Compact Sources ◽  
Astrophysical Research

AbstractCompact objects are of great interest in astrophysical research. There are active research interests in understanding better various aspects of formation and evolution of these objects. In this paper we addressed some problems related to the compact objects mass limit. We employed Einstein field equations (EFEs) to derive the equation of state (EoS). With the assumption of high densities and low temperature of compact sources, the derived equation of state is reduced to polytropic kind. Studying the polytropic equations we obtained similar physical implications, in agreement to previous works. Using the latest version of Mathematica-11 in our numerical analysis, we also obtained similar results except slight differences in accuracy.

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