Quantum Gravity from Noncommutative Geometry: Black Holes, Gravastars, and the Resolution of Singularities

We present a complete theory of quantum gravity emerging from the noncom-mutative torus T 2θ that previously gave us the masses of elementary particles, thenature of time, and the origin of CP symmetry. The spectral action principle onT 2θ yields modified Einstein equations with a dynamical θ-field that regularizes allclassical singularities.Key results:1. Effective action: From the spectral action derived2. Regular solutions: Spherically symmetric static solutions reveal a critical value Θcrit of the θ-field at the center, separating two phases:· Phase I (Θ0 < Θcrit 0 ): Quasi-classical black holes with horizons, but with the central singularity replaced by a regular Planckian core of radius `Pl.· Phase II (Θ0 > Θcrit 0 ): Gravastars -- compact objects without horizons, entirely regular, with matter concentrated in a thin shell.3. Phase transition: The transition between phases is second-order, with critical exponents derived analytically.4. Thermodynamics: Black hole thermodynamics is modified 5. Observational signatures: Primordial black holes in the mass range 10^10­~10^15 kg exhibit deviations from classical predictions, potentially observable as gamma-ray bursts or gravitational wave echoes.This work completes the geometric unification of physics: the same noncommutative torus that determines particle masses and the arrow of time also governs the structure of compact objects and resolves all singularities.