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.

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.

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 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.

scholarly journals GENERALIZED MODEL FOR Λ DARK ENERGY

2009 ◽  
Vol 18 (03) ◽  
pp. 389-396 ◽  
Author(s):  
UTPAL MUKHOPADHYAY ◽  
P. C. RAY ◽  
SAIBAL RAY ◽  
S. B. DUTTA CHOUDHURY
Keyword(s):  
Dark Energy ◽  
Equation Of State ◽  
Cosmological Model ◽  
A Priori ◽  
State Parameter ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Equation Of State Parameter ◽  
Two Fluid

Einstein field equations under spherically symmetric space–times are considered here in connection with dark energy investigation. A set of solutions is obtained for a kinematic Λ model, viz. [Formula: see text], without assuming any a priori value for the curvature constant and the equation-of-state parameter ω. Some interesting results, such as the nature of cosmic density Ω and deceleration parameter q, have been obtained with the consideration of two-fluid structure instead of the usual unifluid cosmological model.

Anisotropic fluid spheres satisfying the Karmarkar condition

2019 ◽  
Vol 34 (15) ◽  
pp. 1950113 ◽  
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
Ksh. Newton Singh ◽  
Hasrat Hussain Shah
Keyword(s):  
Compact Stars ◽  
Anisotropic Fluid ◽  
Stability Factor ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Suitable Form ◽  
Fluid Spheres ◽  
Interior Solutions ◽  
Tov Equation

In this paper, we present new physically viable interior solutions of the Einstein field equations for static and spherically symmetric anisotropic compact stars satisfying the Karmarkar condition. For presenting the exact solutions, we provide a new suitable form of one of the metric potential functions. Obtained solutions satisfy all the physically acceptable properties of realistic fluid spheres and hence solutions are well-behaved and representing matter distributions are in equilibrium state and potentially stable by satisfying the TOV equation and the condition on stability factor, adiabatic indices. We analyze the solutions for two well-known compact stars Vela X-1 (Mass = 1.77 M[Formula: see text], R = 9.56 km) and Cen X-3 (Mass = 1.49 M[Formula: see text], R = 9.17 km).

COLLAPSING FLUID WITH SELF-SIMILARITY OF THE SECOND KIND IN 2 + 1 GRAVITY

2008 ◽  
Vol 17 (05) ◽  
pp. 725-735 ◽  
Author(s):  
M. R. MARTINS ◽  
M. F. A. DA SILVA ◽  
YUMEI WU
Keyword(s):  
Dimensional Space ◽  
Radial Pressure ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Naked Singularities ◽  
Circular Symmetry ◽  
Global Properties ◽  
Dust Fluid

Anisotropic fluid with self-similarity of the second kind in (2 + 1)-dimensional space–times with circular symmetry is studied. By imposing the condition that the radial pressure vanishes, we show that the only allowed solutions are the ones that represent dust fluid. All such solutions to the Einstein field equations are found and their local and global properties are studied in detail. It is found that some can be interpreted as representing gravitational collapse, in which both naked singularities and black holes can be formed.

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.

scholarly journals EFFECTS OF ELECTROMAGNETIC FIELD ON THE DYNAMICS OF BIANCHI TYPE VI0UNIVERSE WITH ANISOTROPIC DARK ENERGY

2010 ◽  
Vol 19 (12) ◽  
pp. 1957-1972 ◽  
Author(s):  
M. SHARIF ◽  
M. ZUBAIR
Keyword(s):  
Electromagnetic Field ◽  
Dark Energy ◽  
Bianchi Type ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Anisotropic Behavior ◽  
Field Equations ◽  
Future Evolution ◽  
Anisotropic Dark Energy ◽  
The Universe

Spatially homogeneous and anisotropic Bianchi type VI0cosmological models with cosmological constant are investigated in the presence of anisotropic dark energy. We examine the effects of electromagnetic field on the dynamics of the universe and anisotropic behavior of dark energy. The law of variation of the mean Hubble parameter is used to find exact solutions of the Einstein field equations. We find that electromagnetic field promotes anisotropic behavior of dark energy which becomes isotropic for future evolution. It is concluded that the isotropic behavior of the universe model is seen even in the presence of electromagnetic field and anisotropic fluid.

scholarly journals Static traversable wormholes in Lyra manifold

2018 ◽  
Vol 27 (03) ◽  
pp. 1850024 ◽  
Author(s):  
A. Sayahian Jahromi ◽  
H. Moradpour
Keyword(s):  
Dark Energy ◽  
Vector Field ◽  
Displacement Vector ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Asymptotically Flat ◽  
Lyra Manifold ◽  
Displacement Vector Field ◽  
Traversable Wormholes

At first, considering the Einstein framework, we introduce some new static traversable wormholes and study the effects of a dark energy-like source on them. Thereinafter, a brief review on Einstein field equations in Lyra manifold is presented, and we address some static traversable wormholes in the Lyra manifold which satisfy the energy conditions. It is also shown that solutions introduced in the Einstein framework may also meet the energy conditions in the Lyra manifold. Finally, we focus on vacuum Lyra manifold and find some traversable asymptotically flat wormholes. In summary, our study shows that it is theoretically possible to find a Lyra displacement vector field in a manner in which traversable wormholes satisfy the energy conditions in a Lyra manifold.

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