Dynamic Rigid Fractal Spacetime Manifold Theory Mathematical Framework, Analysis, and Experiments

The singularity problem in general relativity and the challenges of quantumgravity at the Planck scale remain unresolved. This paper proposes a unified frame?work based on the Dynamic Rigid Fractal Spacetime Manifold Theory (DRFSMT),which avoids singularities in black holes and cosmology through recursive geometricstructures and strict constraint conditions, while offering experimentally verifiablepredictions consistent with observations. The model replaces singularities with afinite fractal core through a recursive hierarchical ”spreading mechanism,” ensuringthe convergence of curvature and energy density. We derive modified Einstein fieldequations, analyze the model’s impact on quasi-normal modes (QNMs), black holeshadow shifts, and cosmic microwave background (CMB) fluctuations, and validateits high consistency with current observational data through numerical simulations.This work not only offers a solution to the singularity problem but also provides anew perspective for bridging quantum gravity and classical general relativity.