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

Abstract

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.

Homothetic congruences in general relativity

“…My aim is to examine the effects of the spacetime generated by a static charged black hole on the aforementioned congruence by means of the generalized values in Eqs. (20) and (21). These generalized components, because of their dependence on the electromagnetic energy-momentum tensor, would therefore show the effect of the black hole's charge on the congruence, despite its electrical neutrality.…”

“…In a group theoretical approach, the spacetime symmetries can also be discussed by means of homothetic vector fields [16,17]. To address further applications, its is worth noting their ability to classify cosmological models in general relativity and alternative gravity [18][19][20][21].…”