Studies On The Traversable Wormhole In The Generalized Brans-Dicke Theory

Given that there are some questions on the general relativity,including the theoretical and the observational aspects,it is significant to investigate the modified gravitational theories.Lots of modified gravitational theories have been constructed,such as the f(R)theory,the f(T)theory,the f(G)theory,the extra-dimension theory,and so on.In this thesis,we study a modified gravitational theory,called the generalized Brans-Dicke theory(GBD).In the first part of this work,we introduce the history of the wormhole physics briefly.In the chapter 2 of this paper,we introduce the wormhole in the Brans-Dicke theory with the Jordan frame and the Einstein frame,respectively.Section 3 describes a modified BD theory(MBD).The MBD theory modified the dynamical term for the BD scalar field,and it can be found that the traversable wormhole can be obtained in this theory with the requirement of violated weak energy condition.The chapter 4 of this paper is our work.We investigate the traversable wormhole in the GBD theory.Firstly,we state the action and the field equation in the GBD modified theory.Secondly,we derive the expressions of the energy density and the pressure for the matter that passing through the wormhole.Choosing two state equations and considering the specific shape function and the scalar-field function,we derive the analytical expression of f(R),and investigate the viable for the derived f(R)function.Finally,we discuss the energy conditions for the matter near to the throat of wormhole in the framework of GBD theory,whose result is different from the result given in the general relativity(GR).In the GR,the null energy condition(NEC)and the weak energy condition(WEC)need to be violated in order to form the traversable wormhole.However,for the considered example in our GBD theory,the NEC and the WEC can be satisfied for the normal matter.The traversable wormhole can be realized by the geometrical quantities in the GBD theory.In addition,it is found that the derived f(R)function,via the reconstructed technique,can be satisfied with the local gravitational experiments and the cosmological constraints.