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