Rotating Black Holes: Continuum Failure Surfaces in Kerr Geometry

This paper extends the substrate stress framework developed for Schwarzschild collapse to the Kerr geometry. The analysis begins with the exact Kerr Kretschmann scalar and expands all polynomial terms explicitly. A stress invariant is defined as σ(r, θ) = √|K(r, θ)|, and a critical value σc is interpreted as the threshold at which the continuum description fails; σc is treated as a phenomenological parameter that characterizes the substrate’s curvature tolerance. The condition σ(r, θ) = σc then determines the failure radius rc(θ), which depends on latitude due to the anisotropic curvature introduced by rotation. The resulting structure is oblate, with its largest radius near the equatorial plane and its smallest radius near the rotation axis. The Kerr ring singularity is never reached within this framework because the stress threshold is encountered at a finite radius. This produces a geometric picture of rotating collapse bounded by a stress-limited surface rather than a classical singularity, and the structure reduces to the Schwarzschild result when the spin parameter is set to zero. This construction yields a covariant framework for analyzing curvature-driven failure in rotating collapse and clarifies how spin modifies the internal geometric structure of black holes.