Gravica

General Relativity computation library built on Symbolica (Rust-powered CAS).

Gravica computes the full GR tensor chain — from metric tensor to Einstein tensor — using Symbolica's high-performance symbolic algebra engine, achieving 23x–4300x speedup over EinsteinPy/SymPy.

Features

• Full GR computation chain: Metric → Christoffel → Riemann → Ricci → Einstein → Weyl
• Curvature invariants: Kretschner scalar, Ricci scalar
• Schouten tensor, Stress-Energy-Momentum tensor
• Geodesic equation generator
• Index raising/lowering utilities
• Built-in metrics: Minkowski, Schwarzschild, Kerr, FLRW, Reissner-Nordström, de Sitter, anti-de Sitter, Gödel
• Lazy evaluation with caching
• Cross-validated against EinsteinPy

Documentation

API reference: https://site.jijinbei.jp/gravica/

Quick Start

See tutorials/getting_started.ipynb for a step-by-step guide.

Benchmarks: Gravica vs EinsteinPy

All benchmarks measured on the same machine. Median of 3 runs with GC disabled.

Speedup Heatmap

Absolute Time Comparison

Summary

Metric inverse is ~0.3–0.5x (Python cofactor overhead), but this is amortized by the massive speedups in downstream computations.

Reproduce

uv run benchmarks/run_benchmarks.py    # Run benchmarks
uv run benchmarks/plot_benchmarks.py   # Generate charts

Architecture

MetricTensor → ChristoffelSymbols → RiemannTensor → RicciTensor → EinsteinTensor
                      ↓                   ↓              ↓       → WeylTensor
               GeodesicEquations   KretschnerScalar  SchoutenTensor
                                                              ↓
                                                     StressEnergyTensor

Tests

uv run pytest

Verified properties:

• Minkowski: All tensors $= 0$
• Schwarzschild: $R_{ab} = 0$, $G_{ab} = 0$ (vacuum), $K = 12,r_s^2/r^6$
• Riemann symmetries: $R^a_{\ bcd} = -R^a_{\ bdc}$
• Christoffel known values: $\Gamma^r_{\ tt} = r_s(r-r_s)/(2r^3)$
• de Sitter / anti-de Sitter: Ricci scalar matches analytic values
• Geodesic equations: Free particle in Minkowski
• Index roundtrip: Raise then lower recovers original tensor
• EinsteinPy cross-validation: Christoffel and Ricci match

License

MIT