2+1-dimensional traversable wormholes supported by positive energy

Abstract

We revisit the shapes of the throats of wormholes, including thin-shell wormholes (TSWs) in $2+1-$dimensions. In particular, in the case of TSWs this is done in a flat $2+1-$dimensional bulk spacetime by using the standard method of cut-and-paste. Upon departing from a pure time-dependent circular shape i.e., $r=a\left(t\right)$ for the throat, we employ a dependent closed loop of the form $r=R\left(t,\theta \right),$ and in terms of $R\left(t,\theta \right)$ we find the surface energy density $\sigma$ on the throat. For the specific convex shapes we find that the total energy which supports the wormhole is positive and finite. In addition to that we analyze the general wormhole's throat. By considering a specific equation of $r=R\left(\theta \right)$ instead of $r=r_0=const.,$ and upon certain choices of functions for $R\left(\theta \right)$ we find the total energy of the wormhole to be positive.

8 pages, 9 figures, final version to appear in EPJC

References in corpus (4)

• Traversable wormholes: Some simple examples
• Traversable wormholes from surgically modified Schwarzschild spacetimes
• General formalism for the stability of thin-shell wormholes in 2+1 dimensions
• Flare-out conditions in static thin-shell wormholes

Cited by in corpus (5)

• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Thin shells in (2+1)-dimensional F(R) gravity
• 3+1-dimensional thin-shell wormhole with deformed throat can be supported by normal matter
• Magnetic Morris-Thorne wormhole in 2+1-dimensions
• Thin-shell wormholes in 2+1-dimensional Einstein-Scalar Theory