Exact Spinning Morris-Thorne Wormhole: Causal Structure, Shadows, and Multipole Moments

Abstract

We construct an exact spinning generalisation of the Morris-Thorne traversable wormhole supported by an anisotropic fluid. Within the Teo wormhole ansatz with unit lapse and Morris-Thorne shape function, we solve analytically for the frame-dragging function and obtain a two-parameter family of asymptotically flat solutions labelled by the throat radius $r_0$ and total angular momentum $J$. Curvature scalars and stress-energy components are given in closed form, showing a regular throat, equatorial reflection symmetry, and violations of all standard energy conditions, as required for traversable wormholes. We analyse the causal structure and show that, despite the presence of an ergoregion for sufficiently large $|J|$, the coordinate time defines a global temporal function, so the spacetime is stably causal and free of closed timelike curves. The optical appearance is studied via photon trajectories. The resulting shadows are smaller than Kerr's and depend on the wormhole shape. Finally, we compute the Geroch-Hansen multipole moments and find a massless but spinning configuration with distinctive higher multipoles that encode the throat scale.

Figures (2)

• Figure 1: The shadow of a rotating Morris--Thorne wormhole (solid black line) with shape function $b(r) = r_0^2/r$, and the Kerr black hole (dashed red line) for different spin values and different inclination angles. Here, the mass of the Kerr solution is set to 1 and $r_0 = 2$ for the Morris--Thorne wormhole. The coordinates are in units of mass.
• Figure 2: Cross section of the wormhole throat for a rotating Morris--Thorne wormhole with shape function $b(r) = r_0^2/r$. The solid blue and red curves correspond to the boundary of the ergosphere corresponding to the rescaled spin parameters $j=1$ and $j=3$, respectively, while the solid black line represents the throat of the wormhole.