An exact Kerr-like rotating Morris--Thorne wormhole: throat, ergoregion and equatorial shadow slice

Abstract

We construct an exact Kerr-like rotating extension of the zero-redshift Morris--Thorne wormhole in a Teo-type stationary, axisymmetric ansatz. The Einstein equations for an anisotropic source comoving with zero angular momentum observers fix $\mathcal{K}(r)=r^2+a^2$ and reduce frame dragging to a radial quadrature. For $b(r)=r_0^2/r$, this is evaluated using incomplete elliptic integrals and normalised by the ADM angular momentum. The spacetime is asymptotically flat with zero ADM mass, so $a=J_{\rm ADM}/M_{\rm ADM}$ does not apply. The oblateness length $a$ and angular momentum $J_{\rm ADM}$ remain independent, yielding a family $(r_0,a,J_{\rm ADM})$. The choice $J_{\rm ADM}=ar_0$ selects only a one-parameter slice for numerical ergoregion and equatorial-capture illustrations; it is not a field-equation constraint. We find $r_{\rm th}=\sqrt{r_0^2-a^2}$, with reality bound $|a|\leq r_0$ and regular range $0\leq |a|<r_0$. In the canonical stationary foliation, the throat is defined quasi-locally as the unique closed surface $S_0$ in the family $S_\ell$ with zero mean curvature and positive area second variation. Moreover, $r=r_{\rm th}$ and $\ell=0$ are coordinate representations. A signed throat-adapted coordinate reveals two asymptotically flat ends, excludes closed timelike curves, and establishes that the throat is timelike, not a horizon. These conclusions hold independently of $J_{\rm ADM}=ar_0$. The supporting stress tensor, reconstructed from the Einstein tensor, is an effective phenomenological source. We do not claim any microscopic matter Lagrangian or realistic equation of state. We also determine the ergoregion onset. Since the full Hamilton--Jacobi equation is nonseparable, we limit ourselves to derive the optical result for a one-dimensional equatorial capture interval.