On global properties of certain homogeneous exact solutions of Einstein field equations

2008 ◽  
Vol 49 (5) ◽  
pp. 052502
Author(s):  
M. Ulanovskii
Keyword(s):  
Exact Solutions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Global Properties

scholarly journals Generating solutions to the Einstein field equations

2016 ◽  
Vol 25 (02) ◽  
pp. 1650022 ◽  
Author(s):  
I. G. Contopoulos ◽  
F. P. Esposito ◽  
K. Kleidis ◽  
D. B. Papadopoulos ◽  
L. Witten
Keyword(s):  
Exact Solutions ◽  
Killing Vector ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Physical Interest ◽  
Axisymmetric Solutions

Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this space, the set of potentials associated to a known solution is transformed into a new set, either by continuous transformations or by discrete transformations. In view of this method, and upon consideration of continuous transformations, we arrive at some exact, stationary axisymmetric solutions to the Einstein field equations in vacuum, that may be of geometrical or/and physical interest.

scholarly journals SPIN-1 GRAVITATIONAL WAVES: THEORETICAL AND EXPERIMENTAL ASPECTS

2006 ◽  
Vol 03 (03) ◽  
pp. 451-469 ◽  
Author(s):  
F. CANFORA ◽  
L. PARISI ◽  
G. VILASI
Keyword(s):  
Physical Properties ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Lie Algebra ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Gravitational Fields ◽  
Killing Fields

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

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).

Exact solutions to Einstein field equations

1975 ◽  
Vol 16 (4) ◽  
pp. 958-960 ◽  
Author(s):  
Jorge Melnick ◽  
Romualdo Tabensky
Keyword(s):  
Exact Solutions ◽  
Einstein Field Equations ◽  
Field Equations

KALUZA–KLEIN COSMOLOGICAL MODELS WITH ANISOTROPIC DARK ENERGY

2011 ◽  
Vol 26 (10) ◽  
pp. 739-750 ◽  
Author(s):  
K. S. ADHAV ◽  
A. S. BANSOD ◽  
R. P. WANKHADE ◽  
H. G. AJMIRE
Keyword(s):  
Dark Energy ◽  
Exact Solutions ◽  
Deceleration Parameter ◽  
Hubble Parameter ◽  
Cosmological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Anisotropic Dark Energy ◽  
The Law ◽  
Kaluza Klein

The exact solutions of the Einstein field equations for dark energy in Kaluza–Klein metric under the assumption on the anisotropy of the fluid are obtained by applying the law of variation of Hubble parameter which yields the constant value of deceleration parameter. The isotropy of the fluid, space and expansion are examined.

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.

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.

EINSTEIN FIELD EQUATIONS: AN ALTERNATE APPROACH TOWARDS EXACT SOLUTIONS FOR AN FRW UNIVERSE

2005 ◽  
Vol 20 (11) ◽  
pp. 2481-2484 ◽  
Author(s):  
F. L. WILLIAMS
Keyword(s):  
Exact Solutions ◽  
Recent Work ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Frw Universe ◽  
Friedmann Robertson Walker

We show that the Einstein field equations for a Friedmann-Robertson-Walker(FRW) universe are completely equivalent to a generalized Ermakov-Milne-Pinney system. This extends recent work of R. Hawkins and J. Lidsey, and provides an alternate method for deriving exact solutions of the field equations.

ALGORITHMIC CONSTRUCTION OF EXACT SOLUTIONS FOR NEUTRAL STATIC PERFECT FLUID SPHERES

2013 ◽  
Vol 22 (09) ◽  
pp. 1350052 ◽  
Author(s):  
SUDAN HANSRAJ ◽  
DANIEL KRUPANANDAN
Keyword(s):  
Exact Solutions ◽  
Perfect Fluid ◽  
Complete Solution ◽  
Positive Definiteness ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
New Exact Solutions ◽  
Algorithmic Construction ◽  
Fluid Spacetimes

Although it ranks amongst the oldest of problems in classical general relativity, the challenge of finding new exact solutions for spherically symmetric perfect fluid spacetimes is still ongoing because of a paucity of solutions which exhibit the necessary qualitative features compatible with observational evidence. The problem amounts to solving a system of three partial differential equations in four variables, which means that any one of four geometric or dynamical quantities must be specified at the outset and the others should follow by integration. The condition of pressure isotropy yields a differential equation that may be interpreted as second-order in one of the space variables or also as first-order Ricatti type in the other space variable. This second option has been fruitful in allowing us to construct an algorithm to generate a complete solution to the Einstein field equations once a geometric variable is specified ab initio. We then demonstrate the construction of previously unreported solutions and examine these for physical plausibility as candidates to represent real matter. In particular we demand positive definiteness of pressure, density as well as a subluminal sound speed. Additionally, we require the existence of a hypersurface of vanishing pressure to identify a radius for the closed distribution of fluid. Finally, we examine the energy conditions. We exhibit models which display all of these elementary physical requirements.

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