warpax

JAX tools for curvature, energy conditions, and geodesics in prescribed spacetimes. warpax uses automatic differentiation to evaluate the Einstein tensor, then tests energy conditions across observer directions. See the changelog for version 1.5.0.

Alcubierre wall and speed sweep. Height and color use a signed logarithmic scale; each frame is a separate metric evaluation.

Install and run

Python 3.12 or newer:

pip install warpax

from warpax import certify
from warpax.metrics import RodalMetric

metric = RodalMetric(v_s=0.5, R=1.0, sigma=8.0)
result = certify(metric, shape=(16, 16, 16))
print(result.type_fractions)
print(result.invariant_nec_min)  # Minimum over sampled wall Type-I points.

The grid is a quick demonstration. Resolve the wall and vary the grid before interpreting extrema or type fractions. Geometric units are G = c = 1, with metric signature (-,+,+,+) and float64 enabled at import.

For development and the examples:

git clone https://github.com/anindex/warpax.git
cd warpax
uv sync --locked --extra dev --extra viz --extra design --extra solver
uv run python examples/01_minkowski_sanity.py

What it computes

• Curvature and stress-energy from callable metrics, including ADM fields.
• Hawking–Ellis classification, Type-I eigenvalue margins, and linear matrix inequality (LMI) tests that do not require an algebraic type assignment.
• Continuous observer searches, exact checks for supplied rational certificates, and interval bounds on supported metric domains.
• Timelike and null geodesics, finite-segment energy integrals, tidal effects, and quantum-inequality reference diagnostics.
• Constraint residuals, TOV equilibrium, ADM mass, junction conditions, source-first shell construction, and metric optimization.
• WarpFactory, EinFields, and Cactus imports; Matplotlib and Manim visualization; Bondi flux and Newman–Penrose diagnostics.

Numerical classification and LMI searches use finite precision and tolerances. An unsuccessful certificate search is inconclusive. The exact energy-condition verdict is independent of the observer, but numerical margin magnitudes depend on the tetrad and normalization. Observer optimization also depends on its rapidity cap. The Eulerian normal remains timelike wherever the ADM lapse and spatial metric are valid, including regions where the coordinate vector ∂t is spacelike.

The null integrals cover finite segments. They establish no complete-geodesic ANEC sign or ranking. Grid spreads and polished extrema are numerical diagnostics; only reported interval bounds support continuum claims. Vorticity alone does not determine algebraic type, and the exact pointwise quadratic speed law requires zero momentum and fixed profiles and domains.

Documentation

Start with the quickstart or numbered examples. Each metric implements a callable (4,) -> (4, 4) from spacetime coordinates to the covariant metric tensor.

Example 07 implements a Gaussian warp metric. Examples 08–10 cover shape design and shell diagnostics. Animation commands and system dependencies are in the examples guide and render script.

Checks and reproduction

uv run python -m pytest
uv run ruff check src/ tests/ scripts/ benchmarks/ examples/
uv run ruff format --check src/ tests/ scripts/ benchmarks/ examples/
uv sync --locked --extra docs --extra design
uv run mkdocs build --strict

Tests run in parallel by default. Use -n 2 to limit workers, or select a module such as tests/test_slemma.py.

The script guide lists reproduction commands and required extras. reproduce_all.sh clears generated caches by default; --keep-cache retains them, and --stage selects a stage. Interval enclosures are a separate, expensive stage. The optional paper-number check requires the corresponding manuscript sources and matching numerical inputs.

Citation

Use CITATION.cff for software metadata and cite the relevant paper:

• An T. Le, Observer-robust energy condition verification for warp drive spacetimes (2026).
• An T. Le, On the boundary cost of source-consistent warp shells (2026).

The shell construction and admissibility work belongs to the second paper. See boundary cost for its assumptions.