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 within a Teo-type stationary and axisymmetric ansatz. Imposing the Einstein equations for an anisotropic source comoving with zero angular momentum observers fixes the circumferential metric function to K(r) = r² + a² and reduces the frame-dragging function to a single radial quadrature. For b(r) = r₀²/r, this quadrature is evaluated in terms of incomplete elliptic integrals and normalised by the ADM angular momentum. The spacetime is asymptotically flat but has vanishing ADM mass, so the Kerr relation a = J_ADM/M_ADM is not applicable. The field equations leave the Kerr-like oblateness length a and the physical angular momentum J_ADM independent. The exact family is therefore labelled by (r₀, a, J_ADM). The relation J_ADM = a r₀ is used only to select a one-parameter slice for the numerical ergoregion and equatorial-capture illustrations, and not as a field-equation constraint. We obtain r_th = √(r₀² − a²), the reality bound |a| ⩽ r₀, and the regular range 0 ⩽ |a| < r₀. Within the canonical stationary foliation, the throat is characterised quasi-locally as the unique member S₀ of the closed two-surface family S_ℓ with vanishing mean curvature and positive area second variation. The surfaces r = r_th and ℓ = 0 are only coordinate representations of this surface. A signed throat-adapted coordinate displays two asymptotically flat ends, excludes closed timelike curves, and shows that the throat is timelike rather than a horizon. These geometrical and causal conclusions do not require J_ADM = a r₀. The supporting anisotropic stress tensor is reconstructed from the Einstein tensor and is interpreted here as an effective phenomenological source. No microscopic matter Lagrangian or realistic equation of state is claimed. We also determine the ergoregion onset. Because the full Hamilton–Jacobi equation is not separable, the optical result is only the one-dimensional equatorial capture interval, not the complete two-dimensional shadow.

Keywords

Bibliographic record

BibTeX Citation

@article{Sukaiti2026exactkerrlike,
  author = {Sukaiti, M. E. and Batic, D. and Dutykh, D.},
  title = {An exact Kerr-like rotating Morris–Thorne wormhole: Throat, ergoregion and equatorial shadow slice},
  journal = {Ann. Phys.},
  year = {2026},
  volume = {495},
  pages = {170718},
  doi = {10.1016/j.aop.2026.170718},
  abstract = {We construct an exact Kerr-like rotating extension of the zero-redshift Morris–Thorne wormhole within a Teo-type stationary and axisymmetric ansatz. Imposing the Einstein equations for an anisotropic source comoving with zero angular momentum observers fixes the circumferential metric function to K(r) = r² + a² and reduces the frame-dragging function to a single radial quadrature. For b(r) = r₀²/r, this quadrature is evaluated in terms of incomplete elliptic integrals and normalised by the ADM angular momentum. The spacetime is asymptotically flat but has vanishing ADM mass, so the Kerr relation a = J_ADM/M_ADM is not applicable. The field equations leave the Kerr-like oblateness length a and the physical angular momentum J_ADM independent. The exact family is therefore labelled by (r₀, a, J_ADM). The relation J_ADM = a r₀ is used only to select a one-parameter slice for the numerical ergoregion and equatorial-capture illustrations, and not as a field-equation constraint. We obtain r_th = √(r₀² − a²), the reality bound |a| ⩽ r₀, and the regular range 0 ⩽ |a| < r₀. Within the canonical stationary foliation, the throat is characterised quasi-locally as the unique member S₀ of the closed two-surface family S_ℓ with vanishing mean curvature and positive area second variation. The surfaces r = r_th and ℓ = 0 are only coordinate representations of this surface. A signed throat-adapted coordinate displays two asymptotically flat ends, excludes closed timelike curves, and shows that the throat is timelike rather than a horizon. These geometrical and causal conclusions do not require J_ADM = a r₀. The supporting anisotropic stress tensor is reconstructed from the Einstein tensor and is interpreted here as an effective phenomenological source. No microscopic matter Lagrangian or realistic equation of state is claimed. We also determine the ergoregion onset. Because the full Hamilton–Jacobi equation is not separable, the optical result is only the one-dimensional equatorial capture interval, not the complete two-dimensional shadow.},
  keywords = {rotating wormholes, Morris–Thorne wormholes, exact solutions in general relativity, frame dragging, ergoregions, equatorial shadow slice},
  publisher = {Elsevier BV},
  issn = {0003-4916}
}