More on traversable wormholes sustained by an extra spatial dimension

This paper extends an earlier study by the author [Phys. Rev. D, vol. 98, 064041 (2018), arXiv:1809.01993] in several significant ways. To begin with, the extra spatial dimension is assumed to be time dependent, while the redshift and shape functions, as well as the extra dimension, are functions of both $r$ and $l$, the respective radial and extra coordinates. The main goal is to determine the conditions that allow the throat of the wormhole to be threaded with ordinary matter (by respecting the null energy condition) and that the same conditions lead to a violation of the null energy condition in the fifth dimension, which can therefore be credited with helping to sustain the wormhole. The dependence of the metric coefficients on $l$ and time $t$ may either help or hinder the ability to use ordinary matter, while an unrestricted dependence on the fifth dimension could lead to a curvature singularity at the throat. Finally, the extra dimension may be extremely small or even curled up.