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

TL;DR

This paper constructs an exact model of a spinning traversable wormhole, analyzing its causal structure, shadows, and multipole moments, revealing unique features like regularity, causality, and distinctive optical signatures.

Contribution

It provides an analytical, exact spinning wormhole solution with detailed causal, optical, and multipole analyses, extending previous models.

Findings

The wormhole is regular with a stable causal structure.

Shadows are smaller than Kerr black holes and shape-dependent.

The solution exhibits unique multipole moments indicating a massless but spinning configuration.

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.