TIME-DEPENDENT SOLUTIONS OF 5D VACUUM EINSTEIN EQUATIONS WITH COSMOLOGICAL CONSTANT

2011 ◽  
Vol 26 (22) ◽  
pp. 1673-1679 ◽  
Author(s):  
TAE HOON LEE
Keyword(s):  
Cosmological Constant ◽  
Time Dependence ◽  
Scale Factor ◽  
Einstein Equations ◽  
Time Dependent ◽  
Vacuum Field ◽  
Field Equations ◽  
Vacuum Einstein Equations ◽  
Dimensional Gravity

We solve vacuum field equations in five-dimensional gravity with cosmological constant to determine the time-dependence of the Robertson–Walker scale factor. We discuss its cosmological implications.

scholarly journals The Large Number Hypothesis and Einstein's Theory of Gravitation

1985 ◽  
Vol 38 (4) ◽  
pp. 547 ◽  
Author(s):  
Yun-Kau Lau
Keyword(s):  
Cosmological Model ◽  
Cosmological Constant ◽  
Matter Density ◽  
Time Dependent ◽  
Field Equations ◽  
Large Number Hypothesis ◽  
Theory Of Gravitation ◽  
The Mean ◽  
Limiting Case ◽  
The Universe

In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch.

scholarly journals DARBOUX CLASS OF COSMOLOGICAL FLUIDS WITH TIME-DEPENDENT ADIABATIC INDICES

2000 ◽  
Vol 15 (15) ◽  
pp. 979-990 ◽  
Author(s):  
H. C. ROSU
Keyword(s):  
Mathematical Method ◽  
Cosmological Constant ◽  
Time Dependence ◽  
Adiabatic Index ◽  
Time Dependent ◽  
Accelerating Universe ◽  
Constant Parameter ◽  
Darboux Transformations ◽  
Scale Factors ◽  
Experimental Findings

A one-parameter family of time-dependent adiabatic indices is introduced for any given type of cosmological fluid of constant adiabatic index by a mathematical method belonging to the class of Darboux transformations. The procedure works for zero cosmological constant at the price of introducing a new constant parameter related to the time dependence of the adiabatic index. These fluids can be the real cosmological fluids that are encountered at cosmological scales and they could be used as a simple and efficient explanation for the recent experimental findings regarding the present day accelerating universe. In addition, new types of cosmological scale factors, corresponding to these fluids, are presented.

scholarly journals The universality of vacuum Einstein equations with cosmological constant

1994 ◽  
Vol 11 (6) ◽  
pp. 1505-1517 ◽  
Author(s):  
Marco Ferraris ◽  
Mauro Francaviglia ◽  
Igor Volovich
Keyword(s):  
Cosmological Constant ◽  
Einstein Equations ◽  
Vacuum Einstein Equations

A new family of solutions to Einstein’s vacuum field equations with cosmological constant

2018 ◽  
Vol 33 (21) ◽  
pp. 1850121
Author(s):  
Feng Yang ◽  
Qing-You Sun
Keyword(s):  
Cosmological Constant ◽  
Vacuum Field ◽  
Time Machine ◽  
Field Equations ◽  
New Family ◽  
Modern Cosmology ◽  
Time Periodic Solutions ◽  
Time Periodic ◽  
Time Periodic Solution ◽  
New Time

In this paper, we construct a new time-periodic solution and a new time-machine solution according to the general form of the new family of solutions to the Einstein’s vacuum field equations with cosmological constant. The time-periodic solutions have some relations with the loop universe. The time-machine solutions are spacetime configurations including closed time-like curves (CTCs), and allowing physical observers to return to their own past. This problem has been of concern a lot recently. We expect the new solutions obtained in this paper can be applied in modern cosmology and general relativity.

scholarly journals Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Sanjay Oli
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Gravitational Constant ◽  
Dimensional Space ◽  
Space Time ◽  
Time Dependent ◽  
Field Equations ◽  
Current Observation ◽  
Kinematical Parameters ◽  
Kaluza Klein

We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant (G) and cosmological constant (Λ). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent G and Λ. A variety of solutions have been found in which G increases and Λ decreases with time t, which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.

scholarly journals ON GENERAL SOLUTIONS OF EINSTEIN EQUATIONS

2011 ◽  
Vol 08 (01) ◽  
pp. 9-21 ◽  
Author(s):  
S. VACARU
Keyword(s):  
Partial Differential Equations ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Linear Connection ◽  
Einstein Gravity ◽  
Matter Field ◽  
Einstein Equations ◽  
Deformation Method ◽  
Dimensional Gravity ◽  
Additional Constraints

We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four- and five-dimensional gravity (S. Vacaru, IJGMMP 4 (2007) 1285). In this paper, we prove that such a geometric method can be used for constructing general non-Killing solutions. The key idea is to introduce an auxiliary linear connection which is also metric compatible and completely defined by the metric structure but contains some torsion terms induced nonholonomically by generic off-diagonal coefficients of metric. There are some classes of nonholonomic frames with respect to which the Einstein equations (for such an auxiliary connection) split into an integrable system of partial differential equations. We have to impose additional constraints on generating and integration functions in order to transform the auxiliary connection into the Levi-Civita one. This way, we extract general exact solutions (parametrized by generic off-diagonal metrics and depending on all coordinates) in Einstein gravity and five-dimensional extensions.

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