Spin, Frame-Dragging, and the Angular-Momentum Budget for Orbital Stability in Kerr Spacetime: A Falsifiable, Numerically Validated Reassessment of the Rogue-Planet Hypothesis

Frame-dragging (Lense–Thirring precession) is a well-established consequence of General Relativity: a rotating mass drags nearby inertial frames, and this has been measured directly by Gravity Probe B and the LARES satellites. A separate line of work has speculated, at the level of intuition rather than derivation, that the spin of a celestial body is somehow necessary for sustaining bound orbits around it, and that spin-down could turn bound planets into unbound, "rogue" objects. Taken literally, this claim is false: Schwarzschild spacetime (a = 0) supports perfectly stable bound orbits down to r = 6GM/c², so the absence of central-body spin does not by itself destabilize orbits. This paper replaces that informal claim with a precise, numerically validated one. We integrate the exact equatorial Kerr geodesic equations (symbolic Christoffel symbols, adaptive high-order numerical integration, exact conservation-law-consistent initial conditions) to quantify how the spin a of a central rotating mass changes the angular-momentum budget required for an orbiter to remain bound. We show, with a validated integrator (circular-orbit drift less than 10⁻⁸ over roughly 30 periods) and an ensemble of N = 300 Monte Carlo trials plus a 100-base-sample Saltelli variance decomposition, that (i) an orbit that is exactly circular around a rapidly spinning body (a = 0.9 GM/c) can require angular momentum below the Schwarzschild stability threshold, so that an instantaneous, angular-momentum-conserving spin-down of the central body causes prompt plunge in 36/40 (90%) of the radii tested in our grid; (ii) orbital eccentricity in a perturbed-Kerr ensemble is dominated by the angular-momentum perturbation itself (Sobol first-order index S₁ = 0.83) with spin as a secondary, interaction-heavy factor (S₁ = 0.03, S_T = 0.08); and (iii) this is a strictly local, near-compact-object effect, not a generic mechanism for ordinary star-planet systems, where a/r is much less than 1, making frame-dragging negligible. We recast the rogue-planet connection accordingly: spin-down of a close-in, rapidly rotating primary (e.g. a young star, a white dwarf, a neutron star, or a black hole) can plausibly contribute, alongside dynamical ejection and disk fragmentation, to unbinding a marginal orbiter, whereas the axial spin of the orbiting planet itself is irrelevant to its own orbital confinement. We provide explicit falsifiability criteria, a risk assessment of the framework's assumptions, and a roadmap for observational and computational follow-up.