A class of rigorous solutions for the Bran+Dicke scalar-tensor theory for Einstein-Rosen nonstatic cylindrically symmetric metric is obtained when only scalar field is present (vacuum solutions of Bran+Dicke theory). As the solutions of Brans-Dicke vacuum fields are conformal to either zero-mass scalar field or vacuum solutions of Einstein's gravitational theory, a set of solutions conformal to the above which correspond to zero-mass scalar field has also been obtained.
1. Introduction
The scalar meson field of Yukawa has been introduced into Einstein's general theory of relatively and various aspects of these fields have been studied by many authors [l-lo] in recent years. The scalar field here is an independent source appearing in the energy-momentum-tensor on the right-hand side of the field equations Rij -&gzjR = -KT~~.
(1)
Away from the source, the energy-momentum-tensor Tij is zero. A nonflat solution of the field equations in this case is always attributed to some source of gravitating origin. On the other hand, Yilmaz's [l 1, 121 scalar theory of gravitation excludes the idea of taking the energy-momentum-tensor zero away from the sources. In the source-free region there is a field pervading through space-time which is of zero-mass and the gravitational potentials in this region are functions of this scalar field. The field provides with an energy-momentum-tensor which has some specific form. The scalar-tensor theory of Brans-Dicke [13] is another generalization of the Einstein's theory of relativity. It has been pointed out by Brans [14] that the Einstein theory of relativity does not explain all aspects of Mach's principle. All the Machian effects can be incorporated only if a scalar field is also included in addition to the tensor field in the Einstein's field equations. The philosophy behind the development of the above theory may be seen in "Gravitation and Relativity" as discussed by Dicke [ 151.