Two-fluid Friedmann–Robertson–Walker cosmologies and their numerical predictions

1986 ◽  
Vol 64 (2) ◽  
pp. 204-209 ◽  
Author(s):  
A. A. Coley ◽  
B. O. J. Tupper
Keyword(s):  
Cosmic Microwave Background ◽  
Perfect Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Two Fluids ◽  
Numerical Predictions ◽  
Imperfect Fluid ◽  
State Formula ◽  
Friedmann Robertson Walker

Friedmann–Robertson–Walker models satisfying the Einstein field equations for a combination of two fluids, one of which is a comoving perfect fluid with the radiation equation of state [Formula: see text], representing the cosmic microwave background, are discussed. Existing models, in which the second fluid is a comoving perfect fluid, are reviewed and their numerical predictions calculated. These models are generalized by considering the case in which the second fluid is an imperfect fluid. This fluid is necessarily noncomoving, the tilt representing the motion of the local supercluster of galaxies relative to the cosmic microwave background. The numerical predictions of one such model are calculated and are found to be in excellent agreement with observation.

scholarly journals Friedmann equations for deformed entropic gravity

2020 ◽  
Vol 29 (06) ◽  
pp. 2050042
Author(s):  
Salih Kibaroğlu ◽  
Mustafa Senay
Keyword(s):  
Early Universe ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Frw Universe ◽  
Friedmann Equations ◽  
Entropic Gravity ◽  
The One ◽  
Two Parameters ◽  
Friedmann Robertson Walker

In this study, we investigate the effects of the one- and two-parameters deformed systems on the Friedmann equations of the Friedmann–Robertson–Walker (FRW) universe by using the entropic gravity approach in the framework of the early universe era. We give simplified forms for the deformed Unruh temperature and Einstein field equations for three different deformed systems. Based on these compact equations, we derive the Friedmann equations with the effective gravitational and cosmological terms.

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.

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.

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.

Cosmology

2019 ◽  
pp. 92-100
Author(s):  
Steven Carlip
Keyword(s):  
De Sitter Space ◽  
Red Shift ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Cosmological Solutions ◽  
Expansion Of The Universe ◽  
Topology Of The Universe ◽  
The Universe

Starting with the assumptions of homogeneity and isotropy, the cosmological solutions of the Einstein field equations—the Friedmann-Lemaitre-Robertson-Walker metrics—are derived. After a discussion of constant curvature metrics and the topology of the Universe, the chapter moves on to discuss observational implications: expansion of the Universe, cosmological red shift, primordial nucleosynthesis, the cosmic microwave background, and primordial perturbations. The chapter includes a brief discussion of de Sitter and anti-de Sitter space and an introduction to inflation.

scholarly journals Extended General Relativity for a Curved Universe

2020 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Gravitational Lensing ◽  
Cold Dark Matter ◽  
Positive Curvature ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Cold Dark Matter Model ◽  
Order Of Magnitude ◽  
Dark Matter Model

The Planck Legacy recent release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which confirms the early universe positive curvature with a confidence level exceeding 99%. Besides, the observed gravitational lensing within several galaxy clusters is higher than that estimated through the standard lambda cold dark matter model by an order of magnitude. While general relativity works perfectly well in the present universe where the spacetime is almost flat, it should be enhanced to account for the pre-existing universal curvature. This study presents new enhanced field equations utilising Einstein–Hilbert action. The enhanced field equations are reduced to Einstein field equations in a flat universe.

scholarly journals Extended General Relativity for a Curved Universe

2020 ◽  
Author(s):  
Mohammed B. Al-Fadhli
Keyword(s):  
General Relativity ◽  
Positive Curvature ◽  
Boundary Term ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Microwave Background ◽  
Conformal Curvature ◽  
Curvature Term ◽  
Extended Field ◽  
Matter Energy

The recent Planck Legacy release revealed the presence of an enhanced lensing amplitude in the cosmic microwave background, which endorses the early universe positive curvature with a confidence level exceeding 99%. Although general relativity performs accurately in the present universe where spacetime is almost flat, the necessity of dark matter/energy and the lost boundary term might be signs of its incompleteness. Utilising Einstein–Hilbert action, I present extended field equations considering the pre-existing universal curvatures. The new extended field equations are inclusive of Einstein field equations in addition to the boundary term and the conformal curvature term contributions.

Charged perfect fluid gravitational collapse in f(R, T) gravity

2019 ◽  
Vol 34 (20) ◽  
pp. 1950153 ◽  
Author(s):  
G. Abbas ◽  
Riaz Ahmed
Keyword(s):  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Coupling Parameter ◽  
Apparent Horizon ◽  
Momentum Tensor ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Apparent Horizons ◽  
Spherically Symmetric Metric

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2[Formula: see text]T, where [Formula: see text] is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole.

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