A Python library for simulating and visualizing General Relativistic warp bubble spacetimes.

3D visualization of an Alcubierre warp bubble warping spacetime as a spacecraft travels at the speed of light. The cyan grid shows the distortion of space - contracting in front and expanding behind the bubble. Red regions indicate where exotic matter (negative energy density) would be required.

WarpDrives provides tools for exploring the mathematics of warp drive spacetimes, including:

• Alcubierre (1994): Classic warp bubble with shift vector construction
• Natário (2002): Divergence-free shift vector (expansion-free)
• Van Den Broeck (1999): Pocket modification for energy reduction
• White toroidal: Heuristic toroidal energy distribution [ASSUMPTION]
• Bobrick & Martire (2021): Physical warp drives classification
• Lentz (2021): Soliton warp drive [ASSUMPTION]

Note: This is a mathematical simulation tool. No claims about physical feasibility are made.

The classic Alcubierre metric requires negative energy density (exotic matter) in the bubble wall region:

The red regions indicate where exotic matter is required - a fundamental challenge for physical realization.

Comparison of energy density distributions across all six implemented warp drive metrics:

Test particles follow geodesics through the curved spacetime. Particles near the bubble are "swept along" by the warped space:

The Alcubierre metric creates expansion of space behind the bubble and contraction in front:

Visualization of how the warp bubble distorts the coordinate grid as it propagates:

A clear top-down view showing the spacetime distortion and exotic matter distribution:

Different mathematical functions can define the bubble profile:

Classical energy conditions are violated in the bubble wall:

Bobrick & Martire (2021) showed that subluminal warp drives can use positive energy, while superluminal drives require exotic matter:

Try the warp drive simulator in your browser! Open interactive/index.html to explore warp bubble physics interactively:

• Choose between 4 different warp drive metrics (Alcubierre, Natário, Van Den Broeck, Bobrick-Martire)
• Adjust velocity, bubble radius, and wall thickness in real-time
• Watch spacetime distortion, energy density distribution, and geodesic paths
• Toggle visualization layers: grid distortion, energy density, bubble outline, spacecraft

No installation required - just open the HTML file in any modern browser.

# Clone the repository
git clone https://github.com/mthiel74/WarpDrives.git
cd WarpDrives

# Install with pip
pip install -e .

# Or with development dependencies
pip install -e ".[dev,notebooks]"

from warpbubblesim.metrics import AlcubierreMetric
from warpbubblesim.gr import compute_einstein, compute_energy_density
from warpbubblesim.viz import plot_energy_density
import numpy as np

# Create an Alcubierre warp bubble
metric = AlcubierreMetric(v0=1.0, R=1.0, sigma=8.0)

# Get the metric tensor at a point
g = metric.metric(t=0, x=0, y=0, z=0)
print("Metric at center:", g)

# Compute energy density
metric_func = metric.get_metric_func()
coords = np.array([0, 1, 0.5, 0])  # In the wall region
rho = compute_energy_density(metric_func, coords)
print(f"Energy density: {rho:.4e}")  # Will be negative!

# Visualize
fig, ax = plot_energy_density(metric)
fig.savefig("energy_density.png")

# List available metrics
warpsim list-metrics

# Render field visualizations
warpsim render --metric alcubierre --scenario scenarios/alcubierre_demo.yaml --output out/

# Create geodesic animation
warpsim geodesics --metric alcubierre --output out/geodesics.mp4

# Parameter sweep
warpsim sweep --metric alcubierre --param v0 --values 0.1,0.5,1.0,2.0

from warpbubblesim.metrics import (
    AlcubierreMetric, NatarioMetric, BobrickMartireMetric
)
from warpbubblesim.viz import plot_multiple_fields

metrics = [
    AlcubierreMetric(v0=1.0),
    NatarioMetric(v0=1.0),
    BobrickMartireMetric(v0=0.5),
]

for metric in metrics:
    fig = plot_multiple_fields(metric, save_path=f"out/{metric.citation}.png")

from warpbubblesim.metrics import AlcubierreMetric
from warpbubblesim.gr.geodesics import integrate_geodesic
import numpy as np

metric = AlcubierreMetric(v0=1.0)
metric_func = metric.get_metric_func()

# Initial conditions
x0 = np.array([0.0, -3.0, 0.0, 0.0])  # Start outside bubble
u0 = np.array([1.0, 0.0, 0.0, 0.0])   # Initially at rest

# Integrate
result = integrate_geodesic(metric_func, x0, u0, (0, 10))
print(f"Final position: {result['coords'][-1]}")

from warpbubblesim.metrics import AlcubierreMetric
from warpbubblesim.gr.conditions import check_energy_conditions
import numpy as np

metric = AlcubierreMetric(v0=1.0, R=1.0)
metric_func = metric.get_metric_func()

# Check in the bubble wall
coords = np.array([0, 1.0, 0.3, 0])
conditions = check_energy_conditions(metric_func, coords)

for name, (satisfied, value) in conditions.items():
    status = "SATISFIED" if satisfied else "VIOLATED"
    print(f"{name}: {status} (value: {value:.2e})")

• Metric signature: (-,+,+,+)
• Index ordering: (t,x,y,z) = (0,1,2,3)
• Units: G = c = 1 (geometric units)
• Einstein equations: G_{\mu\nu} = 8\pi T_{\mu\nu}, so T_{\mu\nu} = G_{\mu\nu}/(8\pi)

• Theory - Mathematical foundations and equations
• Metrics - Detailed metric descriptions
• Numerics - Numerical methods
• Visualizations - Visualization guide

Interactive Jupyter notebooks for each metric:

# Run all tests
make test

# Run specific test file
pytest tests/test_minkowski_limit.py -v

WarpDrives/
├── warpbubblesim/
│   ├── gr/          # GR tensor computations
│   ├── metrics/     # Warp drive metric implementations
│   ├── viz/         # Visualization tools
│   └── cli/         # Command-line interface
├── tests/           # Test suite
├── notebooks/       # Jupyter notebooks
├── scenarios/       # YAML configuration files
├── images/          # Generated visualizations
└── docs/            # Documentation

If you use this code in research, please cite:

@software{warpdrives,
  title = {WarpDrives: GR Warp Bubble Spacetime Simulator},
  year = {2024},
  url = {https://github.com/mthiel74/WarpDrives}
}

And the original papers for each metric (see docs/references.bib).

MIT License - see LICENSE for details.

This project implements metrics from:

• Alcubierre (1994)
• Natário (2002)
• Van Den Broeck (1999)
• Bobrick & Martire (2021)
• Lentz (2021)
• White (AIAA papers)

See the documentation for full references.