scholarly journals GRAVITATIONAL COLLAPSE OF SELF-SIMILAR AND SHEAR-FREE FLUID WITH HEAT FLOW

2003 ◽  
Vol 12 (03) ◽  
pp. 347-368 ◽  
Author(s):  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA
Keyword(s):  
Heat Flow ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Free Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Spherical Shells ◽  
Naked Singularities ◽  
Self Similar

A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.

N-DIMENSIONAL GRAVITATIONAL COLLAPSE WITH DARK ENERGY

2008 ◽  
Vol 17 (08) ◽  
pp. 1295-1309
Author(s):  
R. S. GONÇALVES ◽  
JAIME F. VILLAS DA ROCHA
Keyword(s):  
Dark Energy ◽  
Radial Pressure ◽  
The Self ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Naked Singularities ◽  
Self Similar

We study the evolution of an N-dimensional anisotropic fluid with kinematic self-similarity of the second kind and find a class of solutions to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (pr= ωρ) and that the fluid moves along timelike geodesics. As in the four-dimensional case, the self-similarity requires ω = -1. The energy conditions and geometrical and physical properties of the solutions are studied. We find that, depending on the self-similar parameter α, they may represent black holes or naked singularities. We also study the presence of dark energy in some models, and find that their existence gives rise to some constraints on the dimensions of the space–times.

scholarly journals Gravitational collapse of an imperfect nonadiabatic fluid

2014 ◽  
Vol 23 (06) ◽  
pp. 1450056 ◽  
Author(s):  
R. Chan ◽  
M. F. A. da Silva ◽  
C. F. C. Brandt
Keyword(s):  
Apparent Horizon ◽  
Naked Singularity ◽  
Phantom Energy ◽  
Energy Conditions ◽  
Free Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Self Similar ◽  
System Approaches

We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure which is explicitly time-dependent of the fluid is zero and that the fluid moves along timelike geodesics. The energy conditions, geometrical and physical properties of the solutions are studied. The energy conditions are all satisfied at the beginning of the collapse but when the system approaches the singularity the energy conditions are violated, allowing for the appearance of an attractive phantom energy. We have found that, depending on the self-similar parameter α and the geometrical radius, they may represent a naked singularity. We speculate that the apparent horizon disappears due to the emergence of exotic energy at the end of the collapse, or due to the characteristics of null acceleration systems as shown by recent work.

ANISOTROPIC SELF-SIMILAR COSMOLOGICAL MODEL WITH DARK ENERGY

2006 ◽  
Vol 15 (07) ◽  
pp. 991-999 ◽  
Author(s):  
P. R. PEREIRA ◽  
M. F. A. DA SILVA ◽  
R. CHAN
Keyword(s):  
Dark Energy ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Accelerating Universe ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Normal Matter ◽  
Self Similar

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

scholarly journals GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC PERFECT FLUID WITH KINEMATIC SELF-SIMILARITY

2002 ◽  
Vol 11 (02) ◽  
pp. 155-186 ◽  
Author(s):  
C. F. C. BRANDT ◽  
L.-M. LIN ◽  
J. F. VILLAS DA ROCHA ◽  
A. Z. WANG
Keyword(s):  
Black Holes ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Schwarzschild Solution ◽  
Naked Singularities

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav.15, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index α=3/2.

GRAVITATIONAL COLLAPSE OF AN ANISOTROPIC FLUID WITH SELF-SIMILARITY OF THE SECOND KIND

2006 ◽  
Vol 15 (09) ◽  
pp. 1407-1417 ◽  
Author(s):  
C. F. C. BRANDT ◽  
R. CHAN ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA
Keyword(s):  
Black Hole ◽  
Naked Singularity ◽  
Radial Pressure ◽  
The Self ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Self Similar

We study the evolution of an anisotropic fluid with kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (pr = ωρ) and that the fluid moves along time-like geodesics. The self-similarity requires ω = -1. The energy conditions, geometrical and physical properties of the solutions are studied. We have found that, depending on the self-similar parameter α, they may represent a black hole or a naked singularity.

GRAVITATIONAL COLLAPSE OF SPHERICALLY SYMMETRIC ANISOTROPIC FLUID WITH HOMOTHETIC SELF-SIMILARITY

2003 ◽  
Vol 12 (07) ◽  
pp. 1315-1332 ◽  
Author(s):  
C. F. C. BRANDT ◽  
M. F. A. DA SILVA ◽  
JAIME F. VILLAS DA ROCHA ◽  
R. CHAN
Keyword(s):  
Physical Properties ◽  
Gravitational Collapse ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Tangential Pressure

We study spacetimes of spherically symmetric anisotropic fluid with homothetic self-similarity. We find a class of solutions to the Einstein field equations by assuming that the tangential pressure of the fluid is proportional to its radial one and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of these solutions are studied and found that some of them represent gravitational collapse of an anisotropic fluid.

scholarly journals Spacetime Junctions and the Collapse to Black Holes in Higher Dimensions

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Filipe C. Mena
Keyword(s):  
Black Holes ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Gravitational Collapse ◽  
Higher Dimensions ◽  
Fluid Solution ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Naked Singularities ◽  
Geometrical Properties

We review recent results about the modelling of gravitational collapse to black holes in higher dimensions. The models are constructed through the junction of two exact solutions of the Einstein field equations: an interior collapsing fluid solution and a vacuum exterior solution. The vacuum exterior solutions are either static or containing gravitational waves. We then review the global geometrical properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. In the case of radiating exteriors, we show that the data at the boundary can be chosen to be, in some sense, arbitrarily close to the data for the Schwarzschild-Tangherlini solution.

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.

Relativistic modeling of Vela X-1 using the Karmarkar condition

2019 ◽  
Vol 34 (20) ◽  
pp. 1950157 ◽  
Author(s):  
Satyanarayana Gedela ◽  
Ravindra K. Bisht ◽  
Neeraj Pant
Keyword(s):  
Neutron Star ◽  
Physical Properties ◽  
Exact Solutions ◽  
Density Ratio ◽  
Stellar Model ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Parametric Class ◽  
Surface Redshift

The objective of this work is to explore a new parametric class of exact solutions of the Einstein field equations coupled with the Karmarkar condition. Assuming a new metric potential [Formula: see text] with parameter (n), we find a parametric class of solutions which is physically well-behaved and represents compact stellar model of the neutron star in Vela X-1. A detailed study specifically shows that the model actually corresponds to the neutron star in Vela X-1 in terms of the mass and radius. In this connection, we investigate several physical properties like the variation of pressure, density, pressure–density ratio, adiabatic sound speeds, adiabatic index, energy conditions, stability, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent conformity with the already available evidences in theory. Further, we study the variation of physical properties of the neutron star in Vela X-1 with the parameter (n).

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