Hyperbolic Completion of Newton's Off-Center Orbit Problem: Constant-Curvature Rigidity, $SO(2,1)$ Symmetry, and Magnetic Uniqueness

Dipesh Bhandari

The hyperbolic potential $$V(r)=-\frac{\alpha }{(R^2-r^2{)}^2}$$ was identified by Olshanii as the negative-curvature counterpart of Newton's off-center circular-orbit problem. We first sh…