Dust static plane symmetric solutions and their conformal vector fields in f(R) theory of gravity

Abstract

We first find the dust solutions of static plane symmetric spacetimes in the theory of f(R) gravity. Then using the direct integration technique on the solutions obtained, we deduce the conformal vector fields. This is performed in the context of f(R) theory of gravity. There exist six cases. Out of these, in five cases the spacetimes become conformally flat and admit 15 conformal vector fields, whereas in the sixth case, conformal vector fields become Killing vector fields.

Characterizations of vacuum solutions of f(R) − gravity in space-times admitting Z tensor of Codazzi type

“…Moreover, it is applied in [39] the non-vacuum field equations of f (R) to a spherically symmetric space-time having an unequal metric potential. It is also worth mentioning that investigations of conformal symmetries for some remarkable space-times in the f (R)-gravity, such as static plane symmetric space-times, static spherically symmetric spacetimes, static cylindrically symmetric space-times, spatially homogeneous rotating space-times, Bianchi type II space-times, Kantowski-Sachs symmetric space-times, and non-static plane symmetric space-times, were realized in [40][41][42][43][44][45][46]). In the papers just mentioned, the authors found solutions of field equations using different fluid matters in the f (R)-gravity and obtained conformal vector fields for the derived solutions using some algebraic techniques.…”

Classification of static spherically symmetric perfect fluid space-times via conformal vector fields in f(T) gravity

“…The CS also gives a deep insight into the space-time geometry that further helps to describe the associated kinematics as well as dynamics. With these properties, special attention has been given to the study of the CVFs in MTs of gravitation in the last few years [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88]. Continuing this stream of work, we are conducting a study to classify the static SS perfect fluid space-times via CVFs in the f (T) theory of gravity.…”