An Approximate Solution of the Vacuum Static Case of Spherical Symmetry in Brans-Dicke Theory

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Abstract
Starting from the usual variational principle, the gravitational field equations for the vacuum static case of spherical symmetry are obtained in Brans‐Dicke [Phys. Rev. 124, 925 (1961)] scalar‐tensor theory following a technique due to Weyl [H. Weyl, Space‐Time‐Matter (Dover, New York, 1922)]. The field equations being highly nonlinear, an approximate solution to the second order is presented. It is observed that the results of gravitational redshift, deflection of light, and the rotation of the perihelion of Mercury are in agreement with the earlier results obtained by Brans, Dicke, and Heckmann. But the method, being simpler, can be used in solving other problems in the theory.

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