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

scholarly journals PARAMETRIC NONHOLONOMIC FRAME TRANSFORMS AND EXACT SOLUTIONS IN GRAVITY

2007 ◽  
Vol 04 (08) ◽  
pp. 1285-1334 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
General Scheme ◽  
Nonlinear Partial Differential Equations ◽  
Killing Vector ◽  
Field Equations ◽  
Finsler Spaces ◽  
Gravitational Field Equations ◽  
Pp Wave ◽  
Physical Consequences

A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.

scholarly journals TELEPARALLEL ENERGY–MOMENTUM DISTRIBUTION OF LEWIS–PAPAPETROU SPACETIMES

2007 ◽  
Vol 22 (06) ◽  
pp. 425-433 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
Energy Density ◽  
Momentum Distribution ◽  
Gravitational Effect ◽  
External Source ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Teleparallel Theory ◽  
Axisymmetric Solutions

In this paper, we find the energy–momentum distribution of stationary axisymmetric spacetimes in the context of teleparallel theory by using Möller prescription. The metric under consideration is the generalization of the Weyl metrics called the Lewis–Papapetrou metric. The class of stationary axisymmetric solutions of the Einstein field equations has been studied by Galtsov to include the gravitational effect of an external source. Such spacetimes are also astrophysically important as they describe the exterior of a body in equilibrium. The energy density turns out to be nonvanishing and well-defined and the momentum becomes constant except along θ-direction. It is interesting to mention that the results reduce to the already available results for the Weyl metrics when we take ω = 0.

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.

scholarly journals PALATINI FORMALISM OF FIVE-DIMENSIONAL KALUZA–KLEIN THEORY

2005 ◽  
Vol 20 (05) ◽  
pp. 345-353 ◽  
Author(s):  
YOU DING ◽  
YONGGE MA ◽  
MUXIN HAN ◽  
JIANBING SHAO
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Palatini Formalism ◽  
Klein Theory ◽  
Kaluza Klein

The Einstein field equations can be derived in n dimensions (n>2) by the variations of the Palatini action. The Killing reduction of five-dimensional Palatini action is studied on the assumption that pentads and Lorentz connections are preserved by the Killing vector field. A Palatini formalism of four-dimensional action for gravity coupled to a vector field and a scalar field is obtained, which gives exactly the same field equations in Kaluza–Klein theory.

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.

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