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.

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).

scholarly journals Relativistic models of thin disks immersed in a Robertson-Walker type spacetime

2013 ◽  
Vol 9 (18) ◽  
pp. 131-140
Author(s):  
Gonzalo García Reyes ◽  
Edwin García-Quintero
Keyword(s):  
Perfect Fluid ◽  
Time Dependent ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Ricci Collineations ◽  
Walker Metric ◽  
Relativistic Models ◽  
Thin Disks

Using the well known “displace, cut and reflect” method used to generate disks from given solutions of Einstein field equations, we construct somerelativistic models of time dependent thin disks of infinite extension made of a perfect fluid based on the Robertson-Walker metric. Two simple families of models of disks based on Robertson-Walker solutions admitting Matter and Ricci collineations are presented. We obtain disks that are inagreement with all the energy conditions.

An intrinsic conformal Lorentz pseudodistance

1981 ◽  
Vol 89 (2) ◽  
pp. 359-371 ◽  
Author(s):  
Michael J Markowitz
Keyword(s):  
Exact Solutions ◽  
Hyperbolic Space ◽  
Causal Structure ◽  
Sufficient Conditions ◽  
Lorentzian Manifold ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
True Distance ◽  
Reasonable Energy

AbstractAn intrinsic pseudodistance dM is associated to the underlying causal structure of a Lorentzian manifold (M, g). An infinitesimal form for dM is defined on the bundle of null vectors over M and is used to prove that, under certain physically reasonable energy conditions, M is conformally hyperbolic, i.e. that dM is a true distance. As a corollary we obtain sufficient conditions for the conformal hyperbolicity of a globally hyperbolic space-time. Some exact solutions of the Einstein field equations are discussed and possible applications to the study of singularities are outlined.

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.

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

EXACT SOLUTIONS OF THE EINSTEIN–MAXWELL EQUATIONS IN CHARGED PERFECT FLUID SPHERES FOR THE GENERALIZED TOLMAN–OPPENHEIMER–VOLKOFF EQUATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350009 ◽  
Author(s):  
LI ZOU ◽  
FANG-YU LI ◽  
HAO WEN
Keyword(s):  
Cosmological Constant ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Maxwell Equations ◽  
Constant Density ◽  
New Exact Solutions ◽  
First Time ◽  
Classical Constant ◽  
Fluid Spheres ◽  
Charged Case

Exact solutions of the Einstein–Maxwell equations for spherically symmetric charged perfect fluid have been broadly studied so far. However, the cases with a nonzero cosmological constant are seldom focused. In the present paper, the Tolman–Oppenheimer–Volkoff (TOV) equations have been generalized from the neutral case of hydrostatic equilibrium to the charged case of hydroelectrostatic equilibrium, and base on it, for the first time we find a series of new exact solutions of Einstein–Maxwell's equations with a nonzero cosmological constant for static charged perfect fluid spheres. Moreover, two special TOV equations and two classical constant density interior solutions are also given.

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

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