A note on teleparallel conformal Killing vector fields in plane symmetric non-static spacetimes

2016 ◽  
Vol 13 (03) ◽  
pp. 1650030 ◽  
Author(s):  
Suhail Khan ◽  
Tahir Hussain ◽  
Gulzar Ali Khan
Keyword(s):  
Vector Fields ◽  
Killing Vector ◽  
Conformal Factor ◽  
Conformal Killing ◽  
Conformal Killing Vector ◽  
Killing Vector Fields ◽  
Plane Symmetric ◽  
Integrability Conditions ◽  
Conformal Killing Vector Fields ◽  
Metric Functions

The aim of this paper is to investigate teleparallel conformal Killing vector fields (CKVFs) in plane symmetric non-static spacetimes. Ten teleparallel conformal Killing’s equations are obtained which are linear in the components of the teleparallel CKVF [Formula: see text]. A general solution of these equations comprising the components of CKVF and conformal factor is presented, which subject to some integrability conditions. For seven particular choices of the metric functions, the integrability conditions are completely solved to get the final form of teleparallel CKVFs and conformal factor. In four different cases we get proper CKVFs, while in the remaining three cases it is shown that teleparallel CKVFs reduce to teleparallel homothetic or teleparallel Killing vector fields.

scholarly journals Concircular vector fields for Kantowski–Sachs and Bianchi type-III spacetimes

2018 ◽  
Vol 15 (08) ◽  
pp. 1850126 ◽  
Author(s):  
Suhail Khan ◽  
Amjad Mahmood ◽  
Ahmad T. Ali
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Bianchi Type ◽  
Killing Vector ◽  
Conformal Killing ◽  
Conformal Killing Vector ◽  
Killing Vector Fields ◽  
Type Iii ◽  
Conformal Killing Vector Fields ◽  
Metric Functions

This paper intends to obtain concircular vector fields (CVFs) of Kantowski–Sachs and Bianch type-III spacetimes. For this purpose, ten conformal Killing equations and their general solution in the form of conformal Killing vector fields (CKVFs) are derived along with their conformal factors. The obtained conformal Killing vector fields are then placed in Hessian equations to obtain the final form of concircular vector fields. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that Kantowski–Sachs and Bianchi type-III spacetimes admit four-, six-, or fifteen-dimensional concircular vector fields. It is established that for Einstein spaces, every conformal Killing vector field is a concircular vector field. Moreover, it is explored that every concircular vector field obtained here is also a conformal Ricci collineation.

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).

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