scholarly journals Solitons and geometrical structures in a perfect fluid spacetime

2020 ◽  
Vol 50 (1) ◽  
pp. 41-53 ◽  
Author(s):  
Adara M. Blaga
Keyword(s):  
Perfect Fluid ◽  
Geometrical Structures ◽  
Perfect Fluid 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.

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.

scholarly journals A perfect-fluid spacetime for a slightly deformed mass

2016 ◽  
Author(s):  
M. Abishev ◽  
K. Boshkayev ◽  
H. Quevedo ◽  
S. Toktarbay
Keyword(s):  
Perfect Fluid ◽  
Perfect Fluid Spacetime

Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime

2020 ◽  
Vol 17 (06) ◽  
pp. 2050083
Author(s):  
Mohd. Danish siddiqi ◽  
Shah Alam Siddiqui
Keyword(s):  
Vector Field ◽  
Perfect Fluid ◽  
Geometrical Structure ◽  
Ricci Soliton ◽  
Soliton Equation ◽  
Potential Vector ◽  
Laplacian Equation ◽  
Gradient Type ◽  
Perfect Fluid Spacetime ◽  
Text Condition

In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal [Formula: see text]-Ricci soliton with torse-forming vector field [Formula: see text]. Condition for the conformal Ricci soliton to be steady, expanding or shrinking are also given. In particular case, when the potential vector filed [Formula: see text] of the soliton is of gradient type, we derive, from the conformal [Formula: see text]-Ricci soliton equation, a Laplacian equation.

scholarly journals A Study of Conformally Flat Quasi-Einstein Spacetimes with Applications in General Relativity

2021 ◽  
Vol 45 (03) ◽  
pp. 477-489
Author(s):  
VENKATESHA ◽  
ARUNA KUMARA
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Ricci Soliton ◽  
Conformally Flat ◽  
Perfect Fluid Spacetime ◽  
Study Application

In this paper we consider conformally flat (QE)4 spacetime and obtained several important results. We study application of conformally flat (QE)4 spacetime in general relativity and Ricci soliton structure in a conformally flat (QE)4 perfect fluid spacetime.

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.

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