Existence of conformal symmetries in locally rotationally symmetric spacetimes: Some covariant results
In this paper, we investigate conformal symmetries in Locally Rotationally Symmetric (LRS) spacetimes using a semitetrad covariant formalism. We establish that a general LRS spacetime, with simultaneous rotation and spatial twist, must contain a conformal Killing vector in the plane spanned by the fluid flow lines and the preferred spatial direction. If this conformal vector is Killing, then these spacetimes are just tilted solutions of class I or class III. We then transparently show the existence of more general conformal Killing vectors and establish covariant relations between different geometric quantities in these spacetimes. We also prove that a null Killing horizon can exist in these spacetimes when they are simultaneously rotating and twisting and the heat flux attains an extremal value. Our results compliment the earlier work of van den Bergh.