Warp Bubble Connection & Curvature

This repository provides:

• A Python script (connection_curvature.py) that:

  1. Loads the warp-bubble metric ansatz from metric_ansatz.tex (fetched at runtime).
  2. Defines the symbols and profile function (f(r,t)).
  3. Constructs the metric tensor (g_{\mu\nu}).
  4. Computes:
     • Christoffel symbols (\Gamma^\rho_{\mu\nu}),
     • Riemann tensor (R^\rho_{\ \sigma\mu\nu}),
     • Ricci tensor (R_{\mu\nu}),
     • Ricci scalar (R).
  5. Exports each result in LaTeX form.

• A LaTeX document (connection_curvature.tex) that organizes:

  1. The metric definition,
  2. Christoffel symbols,
  3. Riemann tensor (or its nonzero components),
  4. Ricci tensor,
  5. Ricci scalar.

---

Requirements

• Python 3.7+
• Sympy
• Requests

Install dependencies via:

pip install sympy requests

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Usage

1. Fetch the metric ansatz
   The script will download the metric definition from the upstream repo:

https://raw.githubusercontent.com/arcticoder/warp-bubble-metric-ansatz/main/metric_ansatz.tex

2. Run the computation

python connection_curvature.py

-   Outputs:
    
    -   `connection_curvature.tex` (LaTeX document)
        
    -   Optionally, intermediate `.tex` files for each tensor (if you modify the script to do so).

3. Compile the LaTeX

pdflatex connection_curvature.tex

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File structure

├── connection_curvature.py    # Main script
├── connection_curvature.tex   # Generated LaTeX document
└── README.md                  # This file

Scope, Validation & Limitations

• Scope: The materials and numeric outputs in this repository are research-stage examples and depend on implementation choices, parameter settings, and numerical tolerances.
• Validation: Reproducibility artifacts (scripts, raw outputs, seeds, and environment details) are provided in docs/ or examples/ where available; reproduce analyses with parameter sweeps and independent environments to assess robustness.
• Limitations: Results are sensitive to modeling choices and discretization. Independent verification, sensitivity analyses, and peer review are recommended before using these results for engineering or policy decisions.