Traversable-Wormhole Physics in GBD Theory of Modified Gravity

The generalized Brans-Dicke theory (GBD), as one of the modified gravitational theories, was proposed previously and some interesting properties were found in this theory. Here we investigate the traversable-wormhole physics for GBD theory. Firstly, we derive the gravitational field equation in the framework of GBD wormhole geometry. The traversable wormhole could be gained in this theory. Secondly, using the classical reconstruction technique we originally derive an Lagrangian function for describing gravity in GBD theory. And the derived Lagrangian function for gravity could be satisfied with the requirement of the viable conditions, such as the local gravity tests and the cosmological constraints, etc. Thus, the viable model for cosmology, local gravity and traversable WH can be unified in a uniform Lagrangian quantity within the framework of GBD theory. Thirdly, given that the violation of the energy conditions (ECs) often induce some problems in theory, we explore the ECs of matter in the traversable wormhole. It is shown that the null EC, the weak EC and the dominated EC for the matter can be satisfied in the traversable-wormhole physics of GBD theory, which are different from the results given in GR. It seems that the theory of GBD owns the more logic technically and consistency formally than the theory of GR. Fourthly, some other properties of GBD traversable WH are explored, such as the total gravitational energy, the volume integral quantifier, the dynamical stability of the anisotropic matter, and the difference of the propagation of sound within the matter configuration. The results support the GBD to provide an interesting candidate for traversable WH.