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.

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 Bounds on higher derivative f(R,□R,T) models from energy conditions

2019 ◽  
Vol 34 (11) ◽  
pp. 1950082 ◽  
Author(s):  
M. Ilyas ◽  
Z. Yousaf ◽  
M. Z. Bhatti
Keyword(s):  
Perfect Fluid ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Ricci Scalar ◽  
Energy Conditions ◽  
Higher Derivative ◽  
Derivative Formula ◽  
Cosmological Solutions ◽  
Walker Metric ◽  
Cosmic Parameters

This paper studies the viable regions of some cosmic models in a higher derivative [Formula: see text] theory with the help of energy conditions (where [Formula: see text], [Formula: see text] and [Formula: see text] are the Ricci scalar, d’Alembert’s operator and trace of energy–momentum tensor, respectively). For this purpose, we assume a flat Friedmann–Lemaître–Robertson–Walker metric which is assumed to be filled with perfect fluid configurations. We take two distinct realistic models that might be helpful to explore stable regimes of cosmological solutions. After taking some numerical values of cosmic parameters, like crackle, snap, jerk (etc.) as well as viable constraints from energy conditions, the viable zones for the under observed [Formula: see text] models are examined.

scholarly journals FLRW-cosmology in generic gravity theories

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Metin Gürses ◽  
Yaghoub Heydarzade
Keyword(s):  
Perfect Fluid ◽  
Gravity Theory ◽  
Fluid Type ◽  
Field Equations ◽  
Walker Metric ◽  
Flrw Cosmology ◽  
Arbitrary Dimensions ◽  
Gravity Theories

AbstractWe prove that for the Friedmann–Lemaitre–Robertson–Walker metric, the field equations of any generic gravity theory in arbitrary dimensions are of the perfect fluid type. The cases of general Lovelock and $${\mathcal {F}}(R, {\mathcal {G}})$$ F ( R , G ) theories are given as examples.

scholarly journals Anisotropic evolution of D-dimensional FRW spacetime

2019 ◽  
Vol 79 (12) ◽  
Author(s):  
Chad Middleton ◽  
Bret A. Brouse ◽  
Scott D. Jackson
Keyword(s):  
Early Time ◽  
Scale Factor ◽  
Accelerated Expansion ◽  
Late Time ◽  
Time Behavior ◽  
Einstein Field Equations ◽  
Fluid Regime ◽  
Field Equations ◽  
Higher Dimensional ◽  
Walker Metric

AbstractWe examine the time evolution of the $$D=d+4$$D=d+4 dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scale factor as a function of the time. The fluid regime solution closely mimics that described by 4D FRW cosmology, offering a late-time behavior for the 3D scale factor after becoming valid in the early universe, and can give rise to a late-time accelerated expansion driven by vacuum energy. This is shown to be preceded by an earlier volume regime solution, which offers a very early-time epoch of accelerated expansion for a radiation-dominated universe for $$d=1$$d=1. The time scales describing these phenomena, including the transition from volume to fluid regime, are shown to fall within a small fraction of the first second when the fundamental constants of the theory are aligned with the Planck time. This model potentially offers a higher-dimensional alternative to scalar-field inflationary theory and a consistent cosmological theory, yielding a unified description of early- and late-time accelerated expansions via a 5D spacetime scenario.

scholarly journals The Kasner brane

2015 ◽  
Vol 30 (34) ◽  
pp. 1550185
Author(s):  
Mark D. Roberts
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Vacuum Solution ◽  
Energy Conditions ◽  
Field Equations ◽  
Einstein Tensor ◽  
Five Dimensions

Solutions are found to field equations constructed from the Pauli, Bach and Gauss–Bonnet quadratic tensors to the Kasner and Kasner brane spacetimes in up to five dimensions. A double Kasner space is shown to have a vacuum solution. Brane solutions in which the bulk components of the Einstein tensor vanish are also looked at and for four-branes a solution similar to radiation Robertson–Walker spacetime is found. Matter trapping of a test scalar field and a test perfect fluid are investigated using energy conditions.

ANISOTROPIC SELF-SIMILAR COSMOLOGICAL MODEL WITH DARK ENERGY

2006 ◽  
Vol 15 (07) ◽  
pp. 991-999 ◽  
Author(s):  
P. R. PEREIRA ◽  
M. F. A. DA SILVA ◽  
R. CHAN
Keyword(s):  
Dark Energy ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Accelerating Universe ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Normal Matter ◽  
Self Similar

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

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 Emergence of a cosmological constant in anisotropic fluid cosmology

2021 ◽  
pp. 2150156
Author(s):  
M. Cadoni ◽  
A. P. Sanna
Keyword(s):  
Cosmological Constant ◽  
Large Scale ◽  
Spatial Scales ◽  
Time Dependent ◽  
Anisotropic Fluid ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Coincidence Problem ◽  
Order Of Magnitude ◽  
Natural Way

In this paper, we investigate anisotropic fluid cosmology in a situation where the space–time metric back-reacts in a local, time-dependent way to the presence of inhomogeneities. We derive exact solutions to the Einstein field equations describing Friedmann–Lemaítre–Robertson–Walker (FLRW) large-scale cosmological evolution in the presence of local inhomogeneities and time-dependent backreaction. We use our derivation to tackle the cosmological constant problem. A cosmological constant emerges by averaging the backreaction term on spatial scales of the order of 100 Mpc, at which our universe begins to appear homogeneous and isotropic. We find that the order of magnitude of the “emerged” cosmological constant agrees with astrophysical observations and is related in a natural way to baryonic matter density. Thus, there is no coincidence problem in our framework.

Analysis of compact stars in logarithmic-corrected R2 gravity

2019 ◽  
Vol 35 (02) ◽  
pp. 1950354 ◽  
Author(s):  
M. Farasat Shamir ◽  
Iffat Fayyaz
Keyword(s):  
Graphical Representation ◽  
Stellar Model ◽  
Compact Stars ◽  
Energy Conditions ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Logarithmic Corrections ◽  
Proposed Model ◽  
Physical Tests ◽  
Surface Redshift

We discuss the existence of compact stars in the context of [Formula: see text] gravity model, where additional logarithmic corrections are assumed. Here, [Formula: see text] is the Ricci scalar and [Formula: see text], [Formula: see text] are constant values. Further, the compact stars are considered to be anisotropic in nature, due to the spherical symmetry and high density. For this purpose, we derive the Einstein field equations by considering Krori–Barua spacetime. For our proposed model, the physical acceptability is verified by employing several physical tests like the energy conditions, Herrera cracking concept and stability condition. In addition to this, we also discuss some important properties such as mass–radius relation, surface redshift and the speed of sound are analyzed. Our results are compared with observational stellar mass data, namely, 4U 1820-30, Cen X-3, EXO 1785-248 and LMC X-4. The graphical representation of obtained solutions provide strong evidences for more realistic and viable stellar model.

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