Quantum Gravity from Noncommutative Geometry: Black Holes, Gravastars, and the Resolution of Singularities
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 ): 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.
noncommutative geometry, spectral triple, quantum gravity, noncommutative torus, theta functions, elliptic curves, black holes, gravastars, singularities, phase transition, critical phenomena, modified gravity, effective action, spectral action principle, heat kernel expansion, Seeley-DeWitt coefficients, torsion, θ-field, dynamical field, spherically symmetric solutions, numerical analysis, shooting method, phase diagram, critical line, critical exponents, mean-field theory, Landau-Ginzburg model, order parameter, correlation length, horizon, event horizon, regular core, Planck scale, Planck length, Planck time, hierarchy of scales, thermodynamics, Hawking temperature, Bekenstein-Hawking entropy, logarithmic corrections, first law, heat capacity, stability, information paradox, black hole evaporation, gamma-ray bursts, gravitational waves, echoes, modified dispersion relations, CMB constraints, primordial black holes, observational signatures, LIGO, Virgo, KAGRA, LISA, Einstein Telescope, Fermi-LAT, CTA, automorphisms, CP symmetry, j-invariant, complex multiplication, torsion points, generations, mass hierarchy, unification, Chamseddine-Connes, Connes' noncommutative geometry, spectral geometry, noncommutative field theory, quantum field theory, renormalization group, path integral, propagator, loop corrections, UV completion, asymptotic safety, string theory, M-theory, holography, AdS/CFT, cosmology, early universe, inflation, dark matter, dark energy, cosmological constant
noncommutative geometry, spectral triple, quantum gravity, noncommutative torus, theta functions, elliptic curves, black holes, gravastars, singularities, phase transition, critical phenomena, modified gravity, effective action, spectral action principle, heat kernel expansion, Seeley-DeWitt coefficients, torsion, θ-field, dynamical field, spherically symmetric solutions, numerical analysis, shooting method, phase diagram, critical line, critical exponents, mean-field theory, Landau-Ginzburg model, order parameter, correlation length, horizon, event horizon, regular core, Planck scale, Planck length, Planck time, hierarchy of scales, thermodynamics, Hawking temperature, Bekenstein-Hawking entropy, logarithmic corrections, first law, heat capacity, stability, information paradox, black hole evaporation, gamma-ray bursts, gravitational waves, echoes, modified dispersion relations, CMB constraints, primordial black holes, observational signatures, LIGO, Virgo, KAGRA, LISA, Einstein Telescope, Fermi-LAT, CTA, automorphisms, CP symmetry, j-invariant, complex multiplication, torsion points, generations, mass hierarchy, unification, Chamseddine-Connes, Connes' noncommutative geometry, spectral geometry, noncommutative field theory, quantum field theory, renormalization group, path integral, propagator, loop corrections, UV completion, asymptotic safety, string theory, M-theory, holography, AdS/CFT, cosmology, early universe, inflation, dark matter, dark energy, cosmological constant
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