Hypocycloidal throat for 2+1-dimensional thin-shell wormholes

TL;DR

This paper explores 2+1-dimensional thin-shell wormholes with non-circular, hypocycloid-shaped throats, demonstrating that such geometries can satisfy energy conditions and analyzing the energy requirements based on the hypocycloid's parameters.

Contribution

It introduces hypocycloid-shaped throats in 2+1-dimensional wormholes, showing their viability and energy characteristics, extending previous work on non-circular wormhole geometries.

Findings

Hypocycloid shapes can form the throat of 2+1-dimensional wormholes.

Energy requirements increase with the frequency of the hypocycloid's roller circle.

Non-circular throats can satisfy energy conditions in 2+1 dimensions.

Abstract

Recently we have shown that for $2+1-$dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider angular dependent throat geometry embedded in a $2+1-$dimensional flat spacetime in polar coordinates. It is shown that a generic, natural example of throat geometry is provided remarkably by a hypocycloid. That is, two flat $2+1-$dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one.