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Construction of a traversable wormhole from a suitable embedding function

Abstract:

In this work, we construct a traversable wormhole by providing a suitable embedding function ensuring the fulfilling of the flaring-out condition. The solution contains free parameters that are reduced through the study of the acceptable conditions of a traversable wormhole. We compute both the quantifier of exotic matter and the quasi-normal modes through the 13th order WKB as a function of the remaining free parameters. We obtain that the wormhole geometry can be sustained by a finite amount of exotic matter and seems to be stable under scalar perturbations.