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.

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 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 Quasilocal conservation laws in cosmology: A first look

2020 ◽  
Vol 29 (14) ◽  
pp. 2043029
Author(s):  
Marius Oltean ◽  
Hossein Bazrafshan Moghaddam ◽  
Richard J. Epp
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Conservation Laws ◽  
Perfect Fluid ◽  
Vacuum Energy ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Stress Energy ◽  
Fluid Matter ◽  
Stress Energy Momentum Tensor

Quasilocal definitions of stress-energy–momentum—that is, in the form of boundary densities (in lieu of local volume densities) — have proven generally very useful in formulating and applying conservation laws in general relativity. In this Essay, we take a basic look into applying these to cosmology, specifically using the Brown–York quasilocal stress-energy–momentum tensor for matter and gravity combined. We compute this tensor and present some simple results for a flat FLRW spacetime with a perfect fluid matter source. We emphasize the importance of the vacuum energy, which is almost universally underappreciated (and usually “subtracted”), and discuss the quasilocal interpretation of the cosmological constant.

scholarly journals Spacetimes Admitting Concircular Curvaure Tensor in f(R) Gravity

2022 ◽  
Vol 9 ◽  
Author(s):  
Uday Chand De ◽  
Sameh Shenawy ◽  
H. M. Abu-Donia ◽  
Nasser Bin Turki ◽  
Suliman Alsaeed ◽  
...  
Keyword(s):  
Energy Density ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Ricci Tensor ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Isotropic Pressure ◽  
Concircular Curvature Tensor ◽  
Fluid Spacetimes

The main object of this paper is to investigate spacetimes admitting concircular curvature tensor in f(R) gravity theory. At first, concircularly flat and concircularly flat perfect fluid spacetimes in fR gravity are studied. In this case, the forms of the isotropic pressure p and the energy density σ are obtained. Next, some energy conditions are considered. Finally, perfect fluid spacetimes with divergence free concircular curvature tensor in f(R) gravity are studied; amongst many results, it is proved that if the energy-momentum tensor of such spacetimes is recurrent or bi-recurrent, then the Ricci tensor is semi-symmetric and hence these spacetimes either represent inflation or their isotropic pressure and energy density are constants.

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.

scholarly journals Bianchi Type I Cosmological Models with Perfect Fluid and Magnetic Field

1985 ◽  
Vol 38 (2) ◽  
pp. 239 ◽  
Author(s):  
SR Roy ◽  
S Narain ◽  
JP Singh
Keyword(s):  
Magnetic Field ◽  
Perfect Fluid ◽  
Bianchi Type ◽  
Unit Vector ◽  
Cosmological Models ◽  
Type I ◽  
Constant Ratio ◽  
Bianchi Type I ◽  
Expansion Scalar

We investigate Bianchi type I cosmological models containing a perfect fluid and with an incident magnetic field directed along the x axis. The solutions obtained represent an expansion scalar B bearing a constant ratio to the anisotropy in the direction of a space-like unit vector At.

scholarly journals On mixed quasi-Einstein spacetimes

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2707-2719
Author(s):  
Young Suh ◽  
Pradip Majhi ◽  
De Chand
Keyword(s):  
Vector Field ◽  
Perfect Fluid ◽  
Thermal Equilibrium ◽  
Vector Fields ◽  
Type I ◽  
Velocity Vector Field ◽  
Lorentzian Metric ◽  
Flat Spacetimes ◽  
Zero Scalar Curvature ◽  
Perfect Fluid Spacetime

The object of the present paper is to study mixed quasi-Einstein spacetimes, briefly M(QE)4 spacetimes. First we prove that every Z Ricci pseudosymmetric M(QE)4 spacetimes is a Z Ricci semisymmetric spacetime. Then we study Z flat spacetimes. Also we consider Ricci symmetric M(QE)4 spacetimes and among others we prove that the local cosmological structure of a Ricci symmetricM(QE)4 perfect fluid spacetime can be identified as Petrov type I, DorO. We show that such a spacetime is the Robertson-Walker spacetime. Moreover we deal with mixed quasi-Einstein spacetimes with the associated generators U and V as concurrent vector fields. As a consequence we obtain some important theorems. Among others it is shown that a perfect fluid M(QE)4 spacetime of non zero scalar curvature with the basic vector field of spacetime as velocity vector field of the fluid is of Segr?e characteristic [(1,1,1),1]. Also we prove that a M(QE)4 spacetime can not admit heat flux provided the smooth function b is not equal to the cosmological constant k. This means that such a spacetime describe a universe which has already attained thermal equilibrium. Finally, we construct a non-trivial Lorentzian metric of M(QE)4.

scholarly journals D-BRANE WORLDS AND THE COSMOLOGICAL CONSTANT

2006 ◽  
Vol 21 (03) ◽  
pp. 213-229
Author(s):  
P. GUSIN ◽  
J. WARCZEWSKI
Keyword(s):  
Energy Density ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Speed Of Sound ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Brane Worlds

The cosmological constant on a D-brane is analyzed. This D-brane is in the background produced by the p-brane solutions. The energy–momentum tensor in this model has been found and the form of the cosmological constant has been derived. This energy–momentum tensor is interpreted as an energy–momentum tensor for a perfect fluid on the D-brane. The energy density and the pressure for this fluid have been derived. As it turned out the pressure is negative but the speed of sound is real.

scholarly journals Curvature tensor for the spacetime of general relativity

2017 ◽  
Vol 14 (05) ◽  
pp. 1750078 ◽  
Author(s):  
Zafar Ahsan ◽  
Musavvir Ali
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Vector Fields ◽  
Killing Vector ◽  
Conformal Killing ◽  
Field Equations ◽  
Text Structures ◽  
Conformal Killing Vector Fields ◽  
Perfect Fluid Spacetime

In the differential geometry of certain [Formula: see text]-structures, the role of [Formula: see text]-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field equations with vanishing [Formula: see text]-tensor have been considered and the existence of Killing and conformal Killing vector fields has been established. Perfect fluid spacetimes with vanishing [Formula: see text]-tensor have also been considered. The divergence of [Formula: see text]-tensor is studied in detail and it is seen, among other results, that a perfect fluid spacetime with conserved [Formula: see text]-tensor represents either an Einstein space or a Friedmann-Robertson-Walker cosmological model.

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.

Sign in / Sign up

Export Citation Format

Share Document