Kinematic self-similar solutions of locally rotationally symmetric spacetimes

Abstract

This paper contains locally rotationally symmetric kinematic self-similar perfect fluid and dust solutions. We consider three families of metrics which admit kinematic self-similar vectors of the first, second, zeroth and infinite kinds, not only for the tilted fluid case but also for the parallel and orthogonal cases. It is found that the orthogonal case gives contradiction both in perfect fluid and dust cases for all the three metrics while the tilted case reduces to the parallel case in both perfect fluid and dust cases for the second metric. The remaining cases give self-similar solutions of different kinds. We obtain a total of seventeen independent solutions out of which two are vacuum. The third metric yields contradiction in all the cases.

Locally Rotationally Symmetric Vacuum Solutions in f(R) Gravity

“…The solution given in Eq. ( 24) coincides to the Kinematics self-similar solution of the first kind for the tilted dust case given in table 1 of the [41].…”

“…where a = e ḡ/2f and b = e g/2f . Hence, this solution corresponds to the Kinematics self-similar solution of the zeroth kind for the parallel vector field case [41]. It is mentioned here that the trivial solution of the Eq.…”

“…It is mentioned here that the Ricci scalar becomes zero for this case. This solution corresponds to the Kinematics self-similar solution of the second kind for the tilted dust case given in table 1 of the [41]. case aI(ii):…”

“…( 11) coincides with the Kinematics self-similar solution of the infinite kind for the parallel dust case given in Eq. ( 39) of [41].…”

“…The LRS spacetimes which contain well-known exact solutions of the EFEs are widely studied by many authors [37]- [41]. It has been shown that they admit a group of motions G 4 acting multiply transitively on three dimensional non-null orbits space-like (S 3 ) or time-like (T 3 ) and the isotropy group is a spatial rotation.…”