Static perfect fluid in Brans-Dicke theory

The static perfect fluid in Brans-Dicke theory with spherical symmetry and conformal flatness leads to a differential equation in terms of the scalar field only. We obtain a unique exact solution for the casep=, but density and pressure are singular at the center. We further consider the metric corresponding to a static nonrotating space-time with two mutually orthogonal spacelike Killing vectors in Brans-Dicke theory. We obtain a differential equation involving only the scalar field for the equation of statep= The general solution is found as a transcendental function. Finally, we generalize a theorem given by Bronnikov and Kovalchuk (1979) for perfect fluid in Einstein's theory.On leave from Jadavpur University, Calcutta-32, India.