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.

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 Petrov types D and II perfect‐fluid solutions in generalized Kerr–Schild form

1988 ◽  
Vol 29 (4) ◽  
pp. 937-944 ◽  
Author(s):  
F. Martín‐Pascual ◽  
J. M. M. Senovilla
Keyword(s):  
Perfect Fluid ◽  
Petrov Types

scholarly journals MODELING USUAL AND UNUSUAL ANISOTROPIC SPHERES

2009 ◽  
Vol 18 (02) ◽  
pp. 275-288 ◽  
Author(s):  
STEFANO VIAGGIU
Keyword(s):  
Perfect Fluid ◽  
Fluid Solution ◽  
Boson Stars ◽  
Perfect Fluid Solution ◽  
Parametric Solutions ◽  
Seed Solution ◽  
Anisotropic Factor ◽  
Anisotropic Spheres ◽  
Free Parameters ◽  
Physical Consequences

In this paper, we study anisotropic spheres built from known static spherical solutions. In particular, we are interested in the physical consequences of a "small" departure from a physically sensible configuration. The obtained solutions smoothly depend on free parameters. By setting these parameters to zero, the starting seed solution is regained. We apply our procedure in detail by taking as seed solutions the Florides metrics, and the Tolman IV solution. We show that the chosen Tolman IV solution, and also the Heint IIa and Durg IV,V perfect fluid solutions, can be used to generate a class of parametric solutions where the anisotropic factor has features recalling boson stars. This is an indication that boson stars could emerge by "perturbing" appropriately a perfect fluid solution (at least for the seed metrics considered). Finally, starting with the Tolman IV, Heint IIa and Durg IV,V solutions, we build anisotropic gravastar-like sources with the appropriate boundary conditions.

scholarly journals SOME PROPERTIES OF THE "STRING GAS" WITH THE EQUATION OF STATE $p = -\frac{1}{3} \rho$

2012 ◽  
Vol 21 (01) ◽  
pp. 1250004 ◽  
Author(s):  
ALEXANDER YU. KAMENSHCHIK ◽  
ISAAK M. KHALATNIKOV
Keyword(s):  
Dark Matter ◽  
Equation Of State ◽  
Perfect Fluid ◽  
Spherically Symmetric ◽  
Rotation Curves ◽  
Matter Effects ◽  
Symmetric Spacetimes ◽  
State Formula ◽  
Spherically Symmetric Spacetimes

We show that the string gas — a perfect fluid with the equation of state [Formula: see text] possesses rather interesting properties. In Friedmann universes its presence can change the observable topology of the space; in the spherically symmetric spacetimes it produces rather bizzare geometries and in a way its influence on the rotation curves mimics the dark matter effects.

Homothetic Ricci collineations in non-static plane symmetric spacetimes with perfect fluid matter

2018 ◽  
Vol 15 (05) ◽  
pp. 1850075
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar
Keyword(s):  
Perfect Fluid ◽  
Ricci Tensor ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Ricci Collineations ◽  
Plane Symmetric ◽  
Symmetric Spacetimes ◽  
Fluid Matter ◽  
Static Plane ◽  
Degenerate Cases

In this paper, we investigate homothetic Ricci collineations (HRCs) for non-static plane symmetric spacetimes. The source of the energy–momentum tensor is assumed to be a perfect fluid. Both degenerate as well as non-degenerate cases are considered and the HRC equations are solved in different cases. It is concluded that these spacetimes may possess 6, 7, 8, 10 or 11 HRCs in non-degenerate case, while they admit seven or infinite number of HRCs for degenerate Ricci tensor.

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.

Sign in / Sign up

Export Citation Format

Share Document