A classification of Bianchi Type I solutions via conformal vector fields and energy conditions in modified teleparallel gravity

Abstract

The focus of this research is to investigate conformal vector fields (CVFs) of Bianchi type I space–times in modified teleparallel gravity (MTG). In order to determine such vector fields, we make a classification of said space–times. As a result, we discover thirty-one distinct Bianchi type I classes in the MTG. With the aid of conformal symmetry adopting a direct integration approach, we thoroughly scrutinize each case and find that the only class that formulates conformally non-flat space–times admits proper CVFs. In the rest of the cases, space–times either become conformally flat or tend to admit homothetic vector fields (HVFs) or Killing vector fields (KVFs). The overall dimension of CVFs for the Bianchi type I space–times in the MTG has turned out to be three, four, five, six, and fifteen. The physical parameters associated with each solution have also been calculated. Moreover, to discuss physically viably resulting solutions, we have to classify the solutions via energy conditions.

Keywords

• Modified teleparallel gravity
• Conformal vector fields
• Direct integration technique
• Bianchi type I space–time