Multi-scale constraints on the rotating Ricci-flat spindle deformation of Kerr: from Solar-System orbits to the black-hole shadow

A new class of Ricci-flat, non-asymptotically flat “spindle” deformations of the Kerr black hole was recently obtained by demagnetizing the Kerr–Bertotti–Robinson solution. The deformation parameter [Formula: see text] is an integration constant, i.e. a property of each central object. We confront the rotating solution with observations of the Sun, the Earth, the double pulsar, Sgr A[Formula: see text], M87[Formula: see text] and stellar-mass black holes. Far from the source the [Formula: see text] deformation is a harmonic quadrupolar tidal potential [Formula: see text]. In the symmetry plane its effect on orbits mimics a cosmological constant [Formula: see text], while inclined orbits acquire an orientation-dependent apsidal precession and a precession of the orbital plane, which we derive from the Gauss and Lagrange equations and verify numerically. A sensitivity analysis with the EPM2017 perihelion uncertainties gives [Formula: see text] (Mars, formal errors), or [Formula: see text]–[Formula: see text] for errors 10–50 times larger. The periastron of S2 gives [Formula: see text] for a unit orientation factor ([Formula: see text] for [Formula: see text] of spin orientations). The Cassini Shapiro delay and the double pulsar give independent bounds, whereas light deflection depends on an arbitrary cut-off. The fractional change of the geodetic precession, [Formula: see text], exceeds [Formula: see text] by a factor [Formula: see text]: Gravity Probe B and lunar laser ranging give [Formula: see text] and [Formula: see text], respectively. The frame-dragging rate, referred to locally non-rotating axes, changes only at relative order [Formula: see text], so all weak-field bounds come from the spin-independent sector. In the static sector, the M87[Formula: see text] photon ring and the innermost stable circular orbit give [Formula: see text] and [Formula: see text] for a near-horizon spindle region. Because the spindle closes at [Formula: see text], the exact solution is used throughout as a near-zone model.