Noether symmetries for a class of static plane symmetric solutions in f(T) gravity

It is well known that the Noether symmetry approach is beneficial for searching physically realistic models that are solutions of the Einstein field equations (EFEs). Particularly, the generators obtained via Noether symmetry help to extract conservation laws of physics. The main goal of this study is to investigate the Noether symmetries for a class of static plane symmetric solutions in the f(T) gravity. The f(T) gravity, where T being torsion is one of the potential candidates of modified theories of gravitation. The theory of f(T) gravity seems to provide a theoretical interpretation of the late-time universe acceleration as well as to explain inflationary senecio. With the help of Noether symmetry, we also classified the solutions in terms of conserved quantities that the associated spacetime can admit. The physical and geometrical interpretations of each of the symmetry generators are also presented. It turns out that a class of static plane symmetric solutions in the f(T) gravity admits 5, 6, 8, 9, 11 and 17 Noether symmetries.

Automated summary

The main goal of this study is to investigate the Noether symmetries for a class of static plane symmetric solutions in f(T) gravity and extract conservation laws using these symmetries. It is found that this class of solutions admits 5, 6, 8, 9, 11, and 17 Noether symmetries in f(T) gravity.