2+1-dimensional traversable wormholes supported by positive energy

TL;DR

This paper explores the shapes of 2+1-dimensional traversable wormholes, demonstrating that certain convex and specific angular profiles can be supported by positive, finite energy, challenging the usual negative energy requirement.

Contribution

It introduces a method to analyze wormhole throats with angular dependence in 2+1 dimensions, showing positive energy support for specific shapes and profiles.

Findings

Convex shapes of wormhole throats can have positive total energy.

Angular-dependent profiles can support traversable wormholes with positive energy.

The analysis challenges the notion that negative energy is necessary for wormhole stability.

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 $% \theta -$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.