A gravitational singularity - infinite density, infinite spacetime curvature - is what general relativity's equations predict at the centre of a black hole. The Penrose-Hawking singularity theorems prove this result rigorously within GR.
Every physicist knows GR must break down before the Planck scale. The singularity is not a prediction of nature - it is a signal that the equations need extension. BFUT Paper 26 provides the extension.
Four Anti-Singularity Mechanisms
T4 restoring pressure: The Spaticle free-energy functional's A/R² localisation energy diverges as R → 0. Compressing matter below the condensation scale produces a restoring pressure growing without bound. Infinite compression would require infinite energy.
C|ψ|⁶ higher-order repulsion: At extreme densities, higher-order terms in the condensation functional become significant, representing many-body repulsion in the substrate. These prevent the density from reaching infinity by producing a stable equilibrium at a finite maximum.
J_entrain outward redistribution flux: Organised rotation of infalling matter entrains the substrate, producing an outward redistribution flux through the same rotational entrainment mechanism that explains flat galaxy rotation curves. This partially counteracts inward gravitational flux.
Carrier relaxation: The substrate's finite propagation capacity (τ_obs ≈ 18.6 ms from GW170817) prevents instantaneous collapse - the substrate cannot communicate the collapse event faster than its own propagation limit.
The Four-Region Structure
Instead of a singularity, Paper 26 derives a four-region compact object structure: outer vacuum region (standard GR holds), intermediate transition region (substrate deformation dominates), inner core region (high-density stable condensation), and central equilibrium region (finite maximum density). The event horizon remains intact. The exterior gravitational dynamics are unchanged from GR. Only the interior is physical - no unphysical infinite density.
Download BFUT papers, simulation code, and companion materials: vijayshankarsharma.com/downloads/