Traversable wormholes with like-Casimir complexity supported with arbitrarily small amount of exotic matter

Abstract

In this work we construct traversable wormholes geometries in the framework of the complexity factor. We provide the redshift function of a Casimir traversable wormhole which, in combination with a non-vanishing complexity factor, leads to a traversable wormhole with a minimum amount of exotic matter. The shape function and the embedding diagram are shown and discussed. The tidal accelerations and the time required to get through the wormholes are estimated.

Quasi normal modes of a Casimir--like traversable wormhole through the semi-analytical WKB approach

“…In this section, we show and discuss the response of the Casimir-like TW in [41] to scalar perturbations.…”

“…The model we are interesting in here corresponds to the TW with Casimir-like complexity supported by a arbitrarily small amount of exotic matter which metric is given by [41]…”

“…It is worth mentioning that, the interval above ensures (see [41] for details): i) a finite time of travel while traversing the wormhole, ii) a reasonable values for the radial tidal force and iii) an arbitrarily small amount of exotic matter. Although the solution has been analysed in some detail in [41], in the next section we complement it by exploring its response to scalar perturbations.…”

“…In the next section we introduce the computation of the QNM frequencies by the WKB approximation. Next, in section III, we review the main aspects of the TW with Casimir-like complexity reported in [41]. The results obtained in this work are entirely contained in section IV where we discuss their impact and scope.…”

“…Nevertheless, in this work, we shall implement the semi-analytical WKB approximation reported in [40]. In particular, we analyse the QNM for the TW reported in [41] that fulfills all the basic requirements of a TW, namely, flaring out condition, small tidal forces, reasonable time to traverse the throat and, an arbitrarily small amount of exotic matter. It is worth mentioning that, although the solution in [41] depends on a free parameter which is bounded in accordance to the above mentioned requirements, it is our main goal here to analyse the possibility of refining such an interval by exploring the stability of the scalar perturbation.…”