BRANS – DICKE THEORY IN GÖDEL TYPE SPACE-TIME
Considering cylindrically symmetric spacetimes and its a specific case, Gödel spacetime, we study Brans-Dicke theory and find the identities under which deceleration parameter and scalar field can be calculated. As an example we take a particular case of matter dominant universe. More specifically, we show that a constant curvature cylindrically symmetric spacetime must have a scalar field of exponential type in radial and time coordinates.