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

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.

5 pages, 3 figures accepted for publication in EPJC

References in corpus (5)

• 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
• 2+1-dimensional traversable wormholes supported by positive energy

Cited by in corpus (4)

• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Asymmetric Thin-Shell Wormholes
• Thin-Shells and Thin-Shell Wormholes in New Massive Gravity
• Note on a thin-shell wormhole in extremal Reissner-Nordström geometry