This repository generates the Einstein tensor (G_{\mu\nu}) and the corresponding stress–energy tensor (T_{\mu\nu}) for a warp-bubble metric ansatz. It relies on the connection and curvature definitions produced by the warp-bubble-connection-curvature repo.

• einstein_equations.py

  • Downloads and parses connection_curvature.tex
  • Reconstructs the metric (g_{\mu\nu}), Ricci tensor (R_{\mu\nu}), and scalar curvature (R)
  • Computes [ G_{\mu\nu} = R_{\mu\nu} - \tfrac{1}{2},g_{\mu\nu},R,\quad T_{\mu\nu} = \frac{1}{8\pi},G_{\mu\nu} ]
  • Exports each (T_{\mu\nu}) component to LaTeX in stress_energy.tex

• stress_energy.tex
  A standalone LaTeX document showing [ G_{\mu\nu} = 8\pi,T_{\mu\nu} \quad\text{and}\quad T_{\mu\nu}(x) = \frac{1}{8\pi}G_{\mu\nu}(x) = \begin{pmatrix} T_{00} & T_{01} & \cdots \ \vdots & \ddots & \end{pmatrix} ] with all entries filled in.

• Python 3.7+
• SymPy
• requests

pip install sympy requests

1. Clone the repo:

git clone https://github.com/arcticoder/warp-bubble-einstein-equations.git
cd warp-bubble-einstein-equations

2. Run the script:

python einstein_equations.py

3. Inspect the generated stress_energy.tex and compile it:

pdflatex stress_energy.tex

• 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.