We derive a steady-state warped-disk equation in the full Kerr spacetime to study the tilt dynamics of a thin, viscous accretion disk around a spinning collapsed object. The formulation, based on Pringle’s framework, remains valid for all values of the Kerr parameter $a$, thereby encompassing both Kerr black holes (BHs, $0<a\le 1$) and Kerr naked singularities ($a>1$). By incorporating the exact Keplerian and Lense-Thirring precession frequencies, we analytically obtain the radial tilt equations of the disk without invoking slow-spin or weak-field approximations. Numerical solutions of the resulting equations obtained under realistic boundary conditions reveal significant deviations from slow-spin approximations, particularly in the inner disk where the relativistic effects dominate. In the diffusive regime, we find that for Kerr naked singularities, the tilt profile exhibits distinct inner hump(s) near the radius where the specific angular momentum vanishes—a feature absent for Kerr BHs. Consideration of a tilt in the inner disk could significantly influence the interpretations from observed X-ray spectral, timing, and polarization features, which are crucial to probe the strong gravity regime and to infer the spin of the central object. While such a distinct hump feature alone does not uniquely distinguish Kerr BHs from Kerr naked singularities, their interpretation, in conjunction with constraints on the disk regime, may provide a potential observational handle on the nature of the accreting collapsed object.

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• Classical black holes
• General relativity
• Gravitation
• Accretion disk & black-hole plasma
• Astronomical black holes