Traversable Lorentzian wormhole on the Shtanov-Sahni braneworld with matter obeying the energy conditions
In this paper we have explored the possibility of constructing a traversable wormhole on the Shtanov-Sahni braneworld with a timelike extra dimension. We find that the Weyl curvature singularity at the throat of the wormhole can be removed with physical matter satisfying the NEC $\rho+p \geq 0$, even in the absence of any effective $\Lambda$-term or any type of charge source on the brane. (The NEC is however violated by the effective matter description on the brane arising due to effects of higher dimensional gravity.) Besides satisfying NEC the matter constituting the wormhole also satisfies the Strong Energy Condition (SEC), $\rho+3p \geq 0$, leading to the interesting possibility that normal matter on the brane may be harnessed into a wormhole. Incidentally, these conditions also need to be satisfied to realize a non-singular bounce and cyclic cosmology on the brane\cite{Sahni4} where both past and future singularities can be averted. Thus, such a cyclic universe on the brane, constituted of normal matter can naturally contain wormholes. The wormhole shape function on the brane with a time-like extra dimension represents the tubular structure of the wormhole spreading out at large radial distances much better than in wormholes constructed in a braneworld with a spacelike extra dimension and have considerably lower mass resulting in minimization of the amount of matter required to construct a wormhole. Wormholes in the Shtanov-Sahni (SS) braneworld also have sufficiently low tidal forces, facilitating traversability. Additionally they are found to be stable and exhibit a repulsive geometry. We are left with the intriguing possibilty that both types of curvature singularity can be resolved with the SS model, which we discuss at the end of the concluding section.