A note on classification of cylindrically symmetric non-static space-times according to their teleparallel killing vector fields in the teleparallel theory of gravitation

In this paper, we explored the conservation laws of cylindrically symmetric non-static space-times by using direct integration technique. This classification also covers non-static plane symmetric space-times, static cylindrically symmetric space-times and plane symmetric static space- times. In this paper, we will only present the results of non static cylindrically symmetric and non-static plane symmetric space-times. The results of static cylindrically symmetric space-times and plane static space-times can be found in Shabbir and Khan (Mod Phys Lett A 25:525, 2010). It turns out that the non-static cylindrically symmetric space-times admit four, five, or seven conservation laws. It is important to note that the above space-times admit at least one or at the most four extra conservation laws. (author)