Construction of a traversable wormhole from a suitable embedding function

TL;DR

This paper constructs a traversable wormhole using an embedding function, demonstrating it can be stable and supported by finite exotic matter, with quantification of quasi-normal modes and stability analysis.

Contribution

It introduces a new method for constructing traversable wormholes via embedding functions, analyzing stability and exotic matter requirements.

Findings

Wormhole can be sustained by finite exotic matter

Geometry appears stable under scalar perturbations

Quantified quasi-normal modes using 13th order WKB

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 $13^{th}$ 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.