# Thin-shell toroidal wormhole

## TL;DR

This paper introduces a stable thin-shell toroidal wormhole with a $T^2$ throat, demonstrating partial energy condition violations and comparing it to spherical wormholes, advancing understanding of nontrivial topological structures in spacetime.

## Contribution

It presents a novel stable toroidal wormhole model with partial energy condition violations, contrasting it with spherical wormholes and analyzing their stability and energy properties.

## Key findings

- The toroidal wormhole is stable against throat excitations.
- Not all energy conditions are violated in the toroidal wormhole.
- Violations of energy conditions occur only partially near the throat.

## Abstract

We consider a topologically nontrivial thin-shell wormhole with a throat in the form of a $T^2$ torus. It is shown that: (i)~such a wormhole is stable with respect to excitations of the throat; (ii)~not all energy conditions are violated for such wormholes; (iii)~if any of the energy conditions is violated, this violation occurs only partially in some region near the throat, and in other regions the violation is absent. Also, we discuss the differences between spherical $S^2$ wormholes and toroidal $T^2$ wormholes under investigation.