Traversable wormhole on the brane with non-exotic matter: a broader view

Abstract

Abstract In this article, the possibility of construction of a traversable wormhole on the Randall–Sundrum braneworld with non-exotic matter employing the Kuchowicz potential has been studied. We have obtained the solution for the shape function of the wormhole and studied its properties along with validity of null energy condition. The junction conditions at the surface of the wormhole are used to evaluate the model parameters. We also evaluate the surface density and surface pressure for the wormhole. We study the geometrical nature of the wormhole and consider the radial and tangential tidal constraints on a traveller trying to traverse the wormhole. Besides, a linearized stability analysis is performed to obtain the region of stability for the wormhole. Our analysis, besides giving an estimate for the bulk equation of state (EoS) parameter, imposes restrictions on the brane tension, which is a very essential parameter in braneworld physics, and very interestingly the restrictions imposed by our physically plausible and traversable wormhole model are in conformity with those imposed by other braneworld geometries which are not associated with a wormhole solution. Besides, it is important to study such constraints imposed by geometrical objects such as wormholes on any gravity theory operating at high-energy scales like braneworld, as wormholes are believed to have been formed from massive compact objects of high energy densities. Also, we go on to justify that the possible detection of a wormhole may well indicate that we live on a three-brane universe.