Helicity-supported stationary spacetimes: A class of finite-energy, horizonless, axisymmetric solutions
Francisco S. N. Lobo, Tiberiu Harko
TLDR
Presents a new class of stable, horizonless spacetimes where differential rotation alone generates gravitomagnetism and complex gravitational dynamics.
Key contributions
- Introduces horizonless, axisymmetric spacetimes where differential rotation creates curvature with flat spatial geometry.
- Shows finite tidal forces, gravitomagnetic fields, and global frame-dragging despite zero ADM mass.
- Demonstrates stable circular orbits for particles and linear stability against radial perturbations.
- Describes perturbations propagating as shear waves, similar to Alfvén waves, with a real frequency spectrum.
Why it matters
This research demonstrates that differential rotation can solely maintain regular, asymptotically flat gravitational fields with rich dynamics. It provides a simplified platform to explore gravitomagnetism, tidal effects, and wave phenomena in rotating backgrounds, with applications to astrophysics.
Original Abstract
We construct a class of stationary, axisymmetric, horizonless spacetimes whose curvature is generated entirely by smooth, localised differential rotation $Ω(r)$, while the spatial geometry remains exactly flat. Despite vanishing ADM mass, these helicity-supported configurations exhibit non-trivial curvature, finite tidal forces, and a gravitomagnetic field arising from the radial shear of the rotation. The twisted stationary Killing congruence produces global frame-dragging, including a gravitational Sagnac effect, and the effective potential admits stable circular orbits for null and timelike particles. The tidal tensor gives oscillatory restoring forces, ensuring stability against radial perturbations. Linearising the Einstein equations yields a wave equation for axisymmetric perturbations of $Ω(r)$; the effective potential is positive and localised, the operator is self-adjoint and positive definite, and the frequency spectrum is real, implying linear stability. Perturbations propagate as shear waves analogous to Alfvén waves. These results show that differential rotation alone can sustain a regular, asymptotically flat gravitational field with rich dynamics. This class of spacetimes provides a tractable platform for exploring gravitomagnetism, tidal and wave phenomena in smooth rotating backgrounds, with direct applications to rotating astrophysical structures.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.