Geometric Surgery for Singular Spacetimes and Quasilocal Angular Momentum: Numerical Validation & Python Implementation

This repository contains the full numerical validation of a new geometric-surgery framework for constrained Lorentzian flows, as detailed in the accompanying report. The implementation tests Theorem 5.2 (a generalized angular‑momentum flux formula) in a 1+1D axisymmetric reduction, providing machine‑precision verification of the framework’s mathematical consistency and physical predictions. Key Features Theorem 5.2 Validation: Direct comparison between boundary‑integral and algebraic forms of angular‑momentum change across surgical excision, agreement to ~1e‑16. Clebsch‑Komar Framework: Implementation of the Clebsch‑decomposed vorticity 1‑form V=dΦ+αdβ and its coupling to axisymmetric geometry. Surgical Excision Protocol: Numerical realization of curvature‑triggered excision and gradient‑soliton replacement. Stable Geometric Evolution: Parabolic‑hyperbolic flow with constrained damping, CFL‑compatible time‑stepping, and bounded gradient enforcement. Contents final report.pdf – Final report detailing numerical methods, validation results, and physical interpretation. ang15.py – Full Python implementation: Initialization of Kerr‑like Clebsch fields. Evolution of α(r) and f(r) under modified diffusion. Surgical criterion evaluation and angular‑momentum flux computation. Validation tables and convergence tests. Physical Implications Demonstrates that angular‑momentum change during surgery is not given by a naive volume integral, but by a boundary flux, confirming the essential role of the gradient‑soliton replacement (V+=0). Provides a singularity‑resolving geometric flow that maintains constraint preservation and conservation laws. Offers a bridge to fluid‐dynamic singularity regularization via Clebsch representation. Requirements Python 3.x NumPy, SciPy, Matplotlib Run time: ~2 minutes on standard hardware Usage bash python ang15.py The script outputs: Validation tables comparing Theorem 5.2 forms. Angular‑momentum evolution over λ=1.0. Field profiles and surgical triggers. Citation If this work informs your research, please cite the accompanying report and the theoretical monograph: Rayan D. Peru. (2026). (Monograph) Surgery on Lorentzian Manifolds: A full account of singularity resolution in gravitational collapse, conservation laws for angular momentum, Geometric Vorticity and the final-state problem for rotating black holes. Zenodo. https://doi.org/10.5281/zenodo.18114549.