Weakly Ricci symmetric spacetimes

2017 ◽  
Vol 15 (01) ◽  
pp. 1850007
Author(s):  
Avik De ◽  
Pradip Majhi
Keyword(s):  
Field Equation ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Petrov Type ◽  
Stiff Matter ◽  
Type Formula ◽  
Dark Fluid ◽  
Symmetric Spacetimes ◽  
Perfect Fluid Spacetime ◽  
Symmetric Spacetime

The objective of the present paper is to study weakly Ricci symmetric spacetimes. Among others, we prove that a weakly Ricci symmetric spacetime obeying Einstein’s field equation without cosmological constant represents stiff matter. Moreover, it is shown that the local cosmological structure of a weakly Ricci symmetric perfect fluid spacetime can be identified as Petrov type [Formula: see text], [Formula: see text] or [Formula: see text]. Next, we prove that a dust and dark fluid weakly Ricci symmetric spacetime satisfying Einstein’s field equation without cosmological constant is vacuum. Finally, we show the non-existence of radiation era in such a spacetime.

scholarly journals On a type of spacetimes

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4251-4260
Author(s):  
Young Suh ◽  
Uday De
Keyword(s):  
Perfect Fluid ◽  
State Equation ◽  
Symmetric Spacetimes ◽  
Petrov Types ◽  
Perfect Fluid Spacetime ◽  
Physical Consequences ◽  
Codazzi Type

In the present paper we characterize a type of spacetimes, called almost pseudo Z-symmetric spacetimes A(PZS)4. At first, we obtain a condition for an A(PZS)4 spacetime to be a perfect fluid spacetime and Roberson-Walker spacetime. It is shown that an A(PZS)4 spacetime is a perfect fluid spacetime if the Z tensor is of Codazzi type. Next we prove that such a spacetime is the Roberson-Walker spacetime and can be identified with Petrov types I, D or O[3], provided the associated scalar ? is constant. Then we investigate A(PZS)4 spacetimes satisfying divC = 0 and state equation is derived. Also some physical consequences are outlined. Finally, we construct a metric example of an A(PZS)4 spacetime.

scholarly journals AN EARLY UNIVERSE MODEL WITH STIFF MATTER AND A COSMOLOGICAL CONSTANT

2011 ◽  
Vol 03 ◽  
pp. 254-265 ◽  
Author(s):  
G. OLIVEIRA-NETO ◽  
G. A. MONERAT ◽  
E. V. CORRÊA SILVA ◽  
C. NEVES ◽  
L. G. FERREIRA FILHO
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Scale Factor ◽  
Initial Singularity ◽  
Discrete Energy ◽  
Classical Level ◽  
Stiff Matter ◽  
Expectation Value ◽  
Variational Formalism ◽  
Friedmann Robertson Walker

In the present work, we study the quantum cosmology description of a Friedmann-Robertson-Walker model in the presence of a stiff matter perfect fluid and a negative cosmological constant. We work in the Schutz's variational formalism and the spatial sections have constant negative curvature. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded therefore we compute the discrete energy spectrum and the corresponding eigenfunctions. In the present work, we consider only the negative eigenvalues and their corresponding eigenfunctions. This choice implies that the energy density of the perfect fluid is negative. A stiff matter perfect fluid with this property produces a model with a bouncing solution, at the classical level, free from an initial singularity. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor. We find that it oscillates between maximum and minimum values. Since the expectation value of the scale factor never vanishes, we confirm that this model is free from an initial singularity, also, at the quantum level.

Spacetimes admitting W2-curvature tensor

2014 ◽  
Vol 11 (04) ◽  
pp. 1450030 ◽  
Author(s):  
Sahanous Mallick ◽  
Uday Chand De
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Constant Scalar Curvature ◽  
Momentum Tensor ◽  
Type I ◽  
Expansion Scalar ◽  
Acceleration Vector ◽  
Perfect Fluid Spacetime ◽  
Codazzi Type

The object of this paper is to study spacetimes admitting W2-curvature tensor. At first we prove that a W2-flat spacetime is conformally flat and hence it is of Petrov type O. Next, we prove that if the perfect fluid spacetime with vanishing W2-curvature tensor obeys Einstein's field equation without cosmological constant, then the spacetime has vanishing acceleration vector and expansion scalar and the perfect fluid always behaves as a cosmological constant. It is also shown that in a perfect fluid spacetime of constant scalar curvature with divergence-free W2-curvature tensor, the energy-momentum tensor is of Codazzi type and the possible local cosmological structure of such a spacetime is of type I, D or O.

Generalized Ricci recurrent spacetimes and GRW spacetimes

2021 ◽  
pp. 2150209
Author(s):  
Sudhakar K. Chaubey ◽  
Young Jin Suh
Keyword(s):  
Vector Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Ricci Soliton ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Einstein's Field Equations ◽  
Almost Ricci Soliton ◽  
Perfect Fluid Spacetime ◽  
Fluid Spacetimes

The main goal of this paper is to study the properties of generalized Ricci recurrent perfect fluid spacetimes and the generalized Ricci recurrent (generalized Robertson–Walker (GRW)) spacetimes. It is proven that if the generalized Ricci recurrent perfect fluid spacetimes satisfy the Einstein’s field equations without cosmological constant, then the isotropic pressure and the energy density of the perfect fluid spacetime are invariant along the velocity vector field of the perfect fluid spacetime. In this series, we show that a generalized Ricci recurrent perfect fluid spacetime satisfying the Einstein’s field equations without cosmological constant is either Ricci recurrent or Ricci symmetric. An [Formula: see text]-dimensional compact generalized Ricci recurrent GRW spacetime with almost Ricci soliton is geodesically complete, provided the soliton vector field of almost Ricci soliton is timelike. Also, we prove that a (GR)n GRW spacetime is Einstein. The properties of (GR)n GRW spacetimes equipped with almost Ricci soliton are studied.

Conformal cylindrically symmetric spacetimes in modified gravity

2015 ◽  
Vol 30 (37) ◽  
pp. 1550202 ◽  
Author(s):  
Murat Metehan Türkog̃lu ◽  
Melis Ulu Dog̃ru
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Casimir Force ◽  
Conformal Symmetry ◽  
Vacuum State ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Symmetric Spacetimes ◽  
Cylindrically Symmetric Spacetime ◽  
Symmetric Spacetime

We investigate cylindrically symmetric spacetimes in the context of [Formula: see text] gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle–Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special [Formula: see text] function convenient to [Formula: see text]-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different [Formula: see text] models. Finally, geometrical and physical results of the solutions are discussed.

scholarly journals Sufficient conditions for a pseudosymmetric spacetime to be a perfect fluid spacetime

2021 ◽  
Author(s):  
Peibiao Zhao ◽  
Uday Chand De ◽  
Bülent Ünal ◽  
Krishnendu De
Keyword(s):  
Cosmological Constant ◽  
Scalar Curvature ◽  
Perfect Fluid ◽  
Sufficient Conditions ◽  
Constant Scalar Curvature ◽  
Conformally Flat ◽  
Einstein’S Field Equations ◽  
Field Equations ◽  
Dust Fluid ◽  
Perfect Fluid Spacetime

The aim of this paper is to obtain the condition under which a pseudosymmetric spacetime to be a perfect fluid spacetime. It is proven that a pseudosymmetric generalized Robertson–Walker spacetime is a perfect fluid spacetime. Moreover, we establish that a conformally flat pseudosymmetric spacetime is a generalized Robertson–Walker spacetime. Next, it is shown that a pseudosymmetric dust fluid with constant scalar curvature satisfying Einstein’s field equations without cosmological constant is vacuum. Finally, we construct a nontrivial example of pseudosymmetric spacetime.

scholarly journals EFFECTS OF ELECTROMAGNETIC FIELD ON GRAVITATIONAL COLLAPSE

2009 ◽  
Vol 24 (31) ◽  
pp. 2551-2563 ◽  
Author(s):  
M. SHARIF ◽  
G. ABBAS
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Physical Significance ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Positive Cosmological Constant ◽  
Symmetric Spacetimes ◽  
Apparent Horizons

In this paper, the effect of electromagnetic field has been investigated on the spherically symmetric gravitational collapse with the perfect fluid in the presence of positive cosmological constant. Junction conditions between the static exterior and non-static interior spherically symmetric spacetimes are discussed. We study the apparent horizons and their physical significance. It is found that electromagnetic field reduces the bound of cosmological constant by reducing the pressure and hence collapsing process is faster as compared to the perfect fluid case. This work gives the generalization of the perfect fluid case to the charged perfect fluid. Results for the perfect fluid case are recovered.

scholarly journals CANONICAL TRANSFORMATION FOR STIFF MATTER MODELS IN QUANTUM COSMOLOGY

2011 ◽  
Vol 03 ◽  
pp. 324-328 ◽  
Author(s):  
C. NEVES ◽  
G. A. MONERAT ◽  
E. V. CORRÊA SILVA ◽  
L. G. FERREIRA FILHO ◽  
G. OLIVEIRA-NETO
Keyword(s):  
Cosmological Constant ◽  
Perfect Fluid ◽  
Canonical Transformation ◽  
Quantum Cosmology ◽  
Symplectic Method ◽  
Coordinate Transformations ◽  
Stiff Matter ◽  
Variational Formalism ◽  
Quantum Operators ◽  
Friedmann Robertson Walker

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as quantum operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

Sign in / Sign up

Export Citation Format

Share Document