Concircular vector fields and the Ricci solitons for the LRS Bianchi type-V spacetimes

2020 ◽  
Vol 35 (20) ◽  
pp. 2050169
Author(s):  
Amjad Mahmood ◽  
Ahmad T. Ali ◽  
Suhail Khan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Fluid Models ◽  
Rotationally Symmetric ◽  
Perfect Fluid Models ◽  
Metric Functions ◽  
Type V ◽  
Bianchi Type V

The purpose of this paper is to explore concircular vector fields (CVFs) of locally rotationally symmetric (LRS) Bianchi type-V spacetimes and to investigate whether these CVFs are Ricci soliton vector fields. We first obtained the concircular equations and then solved them by integrating directly. The existence of concircular symmetry imposes restrictions on the metric functions. It is shown that Bianchi type-V spacetimes admit four-, five-, six-, seven-, eight- or fifteen-dimensional CVFs. Further, we studied the Ricci soliton vector fields for all the cases where Bianchi type-V spacetimes admit CVFs. For this purpose, the obtained CVFs are substituted into Ricci soliton equations. These equations imposed further restrictions on metric functions and it is shown in each case that either all or some CVFs are also Ricci soliton vector fields. The gradient of Ricci soliton vector fields are also obtained. It is shown that the metrics that admit CVFs represent physically plausible perfect fluid models under certain conditions.

Bianchi type-V perfect fluid models

1986 ◽  
Vol 18 (1) ◽  
pp. 79-91 ◽  
Author(s):  
B. K. Nayak ◽  
G. B. Bhuyan
Keyword(s):  
Perfect Fluid ◽  
Bianchi Type ◽  
Fluid Models ◽  
Perfect Fluid Models ◽  
Type V ◽  
Bianchi Type V

Proper projective symmetry in LRS Bianchi type V spacetimes

2018 ◽  
Vol 33 (13) ◽  
pp. 1850073 ◽  
Author(s):  
Ghulam Shabbir ◽  
K. S. Mahomed ◽  
F. M. Mahomed ◽  
R. J. Moitsheki
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Riemann Tensor ◽  
Direct Integration ◽  
Killing Vector Fields ◽  
Rotationally Symmetric ◽  
Projective Vector ◽  
Type V ◽  
Bianchi Type V

In this paper, we investigate proper projective vector fields of locally rotationally symmetric (LRS) Bianchi type V spacetimes using direct integration and algebraic techniques. Despite the non-degeneracy in the Riemann tensor eigenvalues, we classify proper Bianchi type V spacetimes and show that the above spacetimes do not admit proper projective vector fields. Here, in all the cases projective vector fields are Killing vector fields.

scholarly journals Causal heat flow in Bianchi type-V Universe

2014 ◽  
Vol 29 (13) ◽  
pp. 1450071
Author(s):  
M. Govender ◽  
S. Thirukkanesh
Keyword(s):  
Temperature Profile ◽  
Bianchi Type ◽  
Irreversible Thermodynamics ◽  
Hydrostatic Equilibrium ◽  
Rotationally Symmetric ◽  
Spatially Homogeneous ◽  
Bianchi Type V Universe ◽  
Type V ◽  
Bianchi Type V

In this paper, we investigate the role of causal heat transport in a spatially homogeneous, locally-rotationally symmetric (LRS) Bianchi type-V cosmological model. In particular, the causal temperature profile of the cosmological fluid is obtained within the framework of extended irreversible thermodynamics. We demonstrate that relaxational effects can alter the temperature profile when the cosmological fluid is out of hydrostatic equilibrium.

Conformal Ricci collineations in LRS Bianchi type V spacetimes with perfect fluid matter

2017 ◽  
Vol 32 (24) ◽  
pp. 1750124 ◽  
Author(s):  
Fawad Khan ◽  
Tahir Hussain ◽  
Sumaira Saleem Akhtar
Keyword(s):  
Perfect Fluid ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Ricci Collineations ◽  
Rotationally Symmetric ◽  
Fluid Matter ◽  
Type V ◽  
Bianchi Type V

Considering the perfect fluid as a source of energy–momentum tensor, we have classified locally rotationally symmetric (LRS) Bianchi type V spacetimes according to their conformal Ricci collineations (CRCs). It is shown that the LRS Bianchi type V spacetimes with perfect fluid matter admit 9- or 15-dimensional Lie algebra of CRCs when the Ricci tensor is non-degenerate, while the group of CRCs is infinite for degenerate Ricci tensor.

scholarly journals Teleparallel conformal Killing vector fields of LRS Bianchi type V spacetimes in teleparallel gravity

2017 ◽  
Vol 14 (03) ◽  
pp. 1750043 ◽  
Author(s):  
Suhail Khan ◽  
Tahir Hussain ◽  
Gulzar Ali Khan
Keyword(s):  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Teleparallel Gravity ◽  
Conformal Killing ◽  
Killing Vector Fields ◽  
Integrability Conditions ◽  
Conformal Killing Vector Fields ◽  
Type V ◽  
Bianchi Type V

The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity (GR). The general solution of teleparallel conformal Killing's equations is found in terms of some unknown functions of [Formula: see text] and [Formula: see text], along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit proper teleparallel CKVF in only one case, while in remaining cases the teleparallel CKVFs reduce to teleparallel Killing vector fields (KVFs). Moreover, it is shown that the LRS Bianchi type V spacetimes do not admit any proper teleparallel homothetic vector field (HVF).

A study of Noether symmetries in LRS Bianchi type V spacetimes

2019 ◽  
Vol 35 (06) ◽  
pp. 2050026 ◽  
Author(s):  
Sumaira Saleem Akhtar ◽  
Tahir Hussain
Keyword(s):  
Conservation Laws ◽  
Lie Algebra ◽  
Bianchi Type ◽  
Noether Symmetry ◽  
Energy Conditions ◽  
Noether Symmetries ◽  
Rotationally Symmetric ◽  
Symmetry Generators ◽  
Type V ◽  
Bianchi Type V

In this paper, we have studied Noether symmetries of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Solving the determining equations of Noether symmetries, it is concluded that the dimension of Noether algebra for these spacetimes is 5, 6, 7, 9, 10, 11 or 17. For all Noether symmetry generators, we have presented the corresponding conservation laws and the Lie algebra. Moreover, some physical implications of the obtained metrics are discussed, which include the study of different energy conditions.

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