As one of the most important modified theories of gravity,Brans-Dickes theory
of gravitation plays
an important role in studying the motions of stars and cosmic evolution,as
well as in explaining cosmic phenomena.
There is no doubt that solutions to Brans-Dickes field equations are of
great significance in this theory. However,it
is very difficult to obtain exact solutions to the Brans-Dickes field
equations in general cases because of the non
linearity of these equations,although some special solutions can be
obtained in some cases. Fortunately,in these
cases that the gravitational field is weak and the source of the
gravitational field moves slowly,one can easily find
approximate solutions to these field equations. In this paper,we aim at the
weakfield approximate solutions to
Brans-Dickes field equations. Firstly,based on the weak gravitational
field,we expand the Brans-Dickes scalar
field and spacetime metric in the corresponding background fields. Then,we
substitute the scalar field and spacetime
metric into Brans-Dickes field equations to get these corresponding
linearized field equations,and we further
simplify one of them using a specific gauge condition. Finally,we solve the
linearized field equations under the
slow-motion condition,and obtain the weak-field,slow-motion approximate
solutions to Brans-Dicke's field equations. These approximation solutions obtained in this paper can provide
useful reference for the teaching and research in Brans-Dicke's theory of gravitation.