On the cuspy structure of rotating wormhole shadows

Abstract We investigate the shadow cast by a rotating traversable wormhole in the Teo class endowed with a general redshift function, with particular emphasis on the emergence of cuspy structures. The shadow boundary is the common envelope of two critical orbit families: unstable circular orbits outside the throat and orbits at the throat itself. The formation of cusps, marking the transition between smooth and cuspy shadow boundaries, only becomes possible when the redshift parameter $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> is allowed to vary. Moreover, we uncover a universal critical value $$\lambda _c=(\sqrt{5}-1)/4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:msqrt> <mml:mn>5</mml:mn> </mml:msqrt> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> that signals the onset of the cusp. A phase diagram characterized by the spin and redshift parameters reveals four distinct morphologies: smooth, cuspy, ears touching, and throat drowning. The morphology of the wormhole shadow may provide observational diagnostics for the different compact objects in future high-resolution imaging observations.