Proper Teleparallel Homothetic Vector Fields in General Cylindrically Symmetric Space-Times in Teleparallel Theory of Gravitation Using Diagonal Tetrads

摘要

In this paper we consider the most general form of non-static cylindrically symmetric space-times in order to study proper teleparallel homothetic vector fields using the direct integration technique and diagonal tetrads.This study also covers static cylindrically symmetric,Bianchi type Ⅰ,non-static and static plane symmetric space-times as well.Here,we will only discuss the cases which do not fall in the category of static cylindrically symmetric,Bianchi type Ⅰ,non-static and static plane symmetric space-times.From the above study we show that very special classes of the above space-times yield 6,7 and 8 teleparallel homothetic vector fields with non-zero torsion.