Computational Modelling and Numerical Analysis of Spacetime Curvature and Relativistic Gravitational Dynamics in Binary Black Hole Systems

In order to have reliable numerical analysis of archived binary black hole simulations, it is of utmost importance to have a clear physical diagnostics and to have a justification on choosing the reconstruction methods. This study analysed 3,088 orbital records, kept 1,771 trajectory observations, analyzed three curvature snapshots in the adaptive-mesh, and processed 3,088 observations of the most important (2, 2) radiation mode. The separation between the orbital coordinates went down from 10 M to about 1.169926 × 10⁻¹⁰ M. The maximum value of the sampled real Weyl-invariant was 0.163365 at 449.356 M; the maximum value of the sampled real amplitude of Ψ₄ was about 0.000438 at 1080.987429 M. The RMSE for the real part was reduced by 98.752884% and the imaginary part was reduced by 98.754352% for withheld observations within the same waveform when using validation-selected cubic interpolation as compared with a fixed linear interpolation. This comparison gives an auditable and conditional method preference, based on reconstruction error and sampling-density sensitivity. It's not an optimization algorithm or a general-purpose decision support system. Conclusions about the evolution of curvature around the globe or independent prediction of gravitational wave are precluded by coordinate dependence, varying spatial coverage, finite radius of extraction and testing with a single simulation. The main contribution will be an evidence-bounded numerical method comparison, included in interpretable simulation diagnostics.