Resolution of Singularities in Grafov's Quantum Theory of Gravity (GQTG): Regular Quantum Cores, S4 Topology, and the Eternal Evolution of the Universe.

Article 19

Title

Resolution of Singularities in Grafov's Quantum Theory of Gravity (GQTG): Regular Quantum Cores, S4 Topology, and the Eternal Evolution of the Universe.

Author

Yuri Grafov, Independent Physicist & Inventor, Moscow, Russia.

Abstract

Grafov's Quantum Theory of Gravity (GQTG) resolves the classical singularities of General Relativity by replacing them with regular, finite quantum cores. This resolution arises naturally from the dynamics of the unifying Ψ-field on the compact S4 topology. The theory predicts smooth metrics, finite maximum density, and stable configurations both in black holes and in cosmology. We present the physical mechanism, an example of the interior metric, stability analysis, and cosmological consequences, including the absence of a beginning or end of the Universe. The results are consistent with previous works (Articles 1-18) and yield testable predictions.

1. Introduction

General Relativity predicts singularities where curvature and density become infinite. These singularities indicate the breakdown of the classical theory at Planck scales. In GQTG, singularities do not exist as fundamental features of spacetime. Instead, the theory introduces regular quantum cores with finite radius and density, supported by the Ψ-field. This approach eliminates both black hole singularities and the initial cosmological singularity while preserving the predictive power of gravity on large scales.

2. The Mechanism of Singularity Resolution

In GQTG, the coordinate singularity at r = 0 is replaced by a regular quantum core of minimum radius r_min. This core is stabilized by the Ψ-field, which generates an effective repulsive contribution at high densities.

The key parameters of the core are:

- Minimum radius: r_min = 8.324 × 10^{-36} m

- Maximum energy density: P_max = 2.655 x 10^{96} kg/m³

These values emerge from the equilibrium conditions of the Ψ-field in the strong-gravity regime. The effective equation of state inside the core reaches w_Ψ = -1.5, violating the strong energy condition and preventing further collapse. The global S4 topology ensures that there is no true center - r = 0 is merely a coordinate artifact.

3. The Metric Near the Quantum Core

For a static, spherically symmetric black hole, we use isotropic coordinates:

ds²=-e^{2v(r)) dt² + e^{2λ(r)} (dr² + r² dΩ²).

Inside the core 

(r < r_min), the density is nearly constant and equal to P_max. The interior solution can be approximated by the Schwarzschild interior metric for a sphere of constant density, modified by the contribution of the Ψ-field. Expanding near r = 0 yields a regular de Sitter-like form:

ds² = - (1 - (8πG P_max / 3) r²) dt² + (1-(8nG P_max/3) r²)^{-1} dr² + r²dΩ²)

All metric components and the scalar curvature remain finite at r = 0. The temporal component g_tt approaches -1, and the radial component g_rr approaches 1, indicating locally flat behavior at the center of the core. The effective cosmological constant inside the core is Λ_eff = 8πG P_max. ensuring finite curvature.

4. Stability of the Quantum Core

Linear perturbation analysis demonstrates that the core is stable against small spherically symmetric perturbations. Setting Ψ = Ψο + δΨ (where Ψo is the background value), the perturbation equation in the effective de Sitter background shows that homogeneous modes oscillate or decay, while inhomogeneous modes with wavelengths larger than the core size remain bounded. This stability arises from the balancing action of the Ψ-field and confirms that the quantum core is a long-lived, physically realizable configuration.

5. Cosmological Implications

In the cosmological sector, the initial singularity is replaced by a regular bounce at a minimum scale factor a_min. The absence of singularities, combined with w = -1.00000 for the effective dark energy component, implies eternal accelerated expansion. The Universe has neither a singular beginning nor a singular end.

The entropy of the Universe is finite (S_max = 1.3 × 10^{123} k_B, consistent with the holographic bound on S4), leading to a soft heat death asymptotic state of very low but non-zero activity sustained by phytons and residual Ψ-field fluctuations.

6. Black Holes and Information Preservation

Black holes in GQTG possess regular quantum cores rather than singularities. This resolves the black hole information paradox: information is stored in the quantum states of the Ψ-field inside the core and can be gradually released during evaporation. The modified Hawking temperature and the existence of stable cores ensure unitary evolution.

7. Conclusions

GQTG provides a consistent and singularity-free description of strong gravity through:

- Regular quantum cores with finite density and radius,

- Global S4 topology without boundaries,

- Dynamics of the Ψ-field that prevents collapse.

The Universe is eternal, undergoing accelerated expansion toward a soft heat death while preserving information globally. This framework unifies quantum gravity, cosmology, and information theory.

PREDICTIONS 

- Modified gravitational wave echoes from black hole mergers (testable by future detectors).

- Specific CMB anomalies (ΔΙ = 2.7) originating from the regular bounce (CMB-S4).

- Persistent phyton background even in the distant future.

- Phytons will be detected in the coming decades (temperature 0.01463 K, concentration 6.35×10⁻⁵ cm⁻³).

- LISA will measure r = 0.0037, n_t = -0.048.

- Euclid and LSST will refine H_0 = 73.01 ± 0.15 and the dark matter profile r⁻².⁵⁰⁰.