Observer-robust energy condition verification for warp drive spacetimes.

warpax uses JAX automatic differentiation to compute exact curvature tensors from analytic warp drive metrics and performs continuous BFGS optimization over the full timelike observer manifold to find worst-case energy condition violations. This goes beyond the standard Eulerian-observer approach (as in WarpFactory) by searching over all physically admissible observers, parameterized by bounded rapidity in stereographic coordinates, to detect violations that axis-aligned sampling can miss.

Geodesic paths through a collapsing Alcubierre warp bubble, computed via WarpAX's autodiff curvature pipeline.

Users can define their own warp manifold by subclassing ADMMetric and run the full verification pipeline. Below, a Gaussian warp bubble (shift = Gaussian envelope instead of the Alcubierre top-hat) is validated on a 24x24x4 grid. The three panels compare SEC margins seen by the Eulerian observer (left) vs the worst-case boosted observer found by BFGS optimization (center). The right panel highlights 356 grid points where the Eulerian frame incorrectly reports SEC as satisfied -- violations only visible to non-Eulerian observers.

SEC comparison for a custom Gaussian warp bubble (v_s = 0.5). Red regions in the right panel are violations missed by Eulerian-only analysis.

See examples/07_custom_warp_metric.py for the full worked example.

conda create -n warpax python=3.12 -y
conda activate warpax
pip install -e ".[dev]"

Run any example:

python examples/01_minkowski_sanity.py

The full reproduction pipeline regenerates all cached results and figures:

bash reproduce_all.sh

Phases can be run individually:

bash reproduce_all.sh --phase 1   # Core computation
bash reproduce_all.sh --phase 2   # Ablation studies
bash reproduce_all.sh --phase 3   # Figure generation

Use --keep-cache to skip cache deletion and only recompute missing results.

pytest                  # ~450 tests
pytest -m "not slow"    # Skip expensive grid tests

Animated 3D visualizations of warp bubble dynamics require the optional manim dependencies and system packages:

# System dependencies (Ubuntu/Debian)
sudo apt install texlive-latex-extra texlive-fonts-recommended dvipng cm-super ffmpeg

# Python dependencies
pip install -e ".[manim]"

# Render all scenes
python scripts/render_all_scenes.py

# Or render individual scenes
bash scripts/render_manim_scenes.sh

Rendered videos and images are written to media/ (not tracked by git).

warpax is organized into six sub-packages:

All metrics implement a common MetricFunction interface: a callable (4,) -> (4,4) mapping coordinates $x^\mu$ to the covariant metric tensor $g_{\mu\nu}$. This enables a uniform autodiff-based curvature pipeline across all spacetimes.