General class of vacuum Brans-Dicke wormholes

Recently, traversable wormhole geometries were constructed in the context of $f(R)$ gravity. The latter is equivalent to a Brans-Dicke theory with a coupling parameter $\omega =0$, which is apparently excluded from the narrow interval, $-3/2<\omega <-4/3$, extensively considered in the literature of static wormhole solutions in vacuum Brans-Dicke theory. However, this latter interval is only valid for a specific choice of an integration constant of the field equations derived on the basis of a post-Newtonian weak field approximation, and there is no reason for it to hold in the presence of compact objects with strong gravitational fields. In this context, we construct a general class of vacuum Brans-Dicke wormholes that include the value of $\omega =0$.

Figure 1

Plot of the energy conditions for $C(\omega )=({\omega }^2+a^2{)}^{-1}$ for $a=1$. In particular, the WEC expressed by condition (19) is given by the solid line; and the NEC, expressed by the condition (20), is given by the dashed curves. For the latter, only the cases of $(s,t)=(0,1)$ and $(s,t)=(1,1)$ of condition (20) are allowed; and are depicted by the small and large peaks, respectively.

Figure 2

Plot of the energy conditions for $C(\omega )=A\exp (-{\omega }^2/2)$, with $A=3\exp (1/2)$. In particular, the WEC expressed by condition (19) is given by the solid line; and the NEC, expressed by the condition (20), is given by the dashed curve. For the latter, only the cases of $(s,t)=(0,1)$ and $(s,t)=(1,1)$ of condition (20) are allowed; and are depicted by the smaller and larger peaks, respectively.