General Relativity Symbolic Utilities

The pystein package contains utilities for computing symbolic utilities for computing various quantities that arise in general relativity. Presently, this package is essentially a sympy extension that computes components of tensors directly.

Installation

The pystein package is available on PyPI, and can be installed via pip:

pip install pystein

Symbolic Tools

The pystein package makes use of sympy to compute symbolic curvature equations (EFE). A sample snippet is below. For more detail see the documentation.

# Imports
import sympy
from sympy.diffgeom import Manifold, Patch
from pystein import coords, metric, curvature
from pystein.utilities import tensor_pow as tpow

# Create metric
M = Manifold('M', dim=2)
P = Patch('origin', M)
theta, phi, a = sympy.symbols('theta phi a', nonnegative=True)
cs = coords.CoordSystem('spherical', P, [theta, phi])
dtheta, dphi = cs.base_oneforms()
ds2 = a ** 2 * (tpow(dtheta, 2) + sympy.sin(theta) ** 2 * tpow(dphi, 2))
g = metric.Metric(twoform=ds2)

# Compute Christoffel Component
curvature.christoffel_symbol_component(0, 1, 0, g)

Numeric Tools

The pystein package contains some limited numerical utilities, including:

• ability to numerically integrate the geodesic equations geodesic.numerical_geodesic
• convenience functions to compute multiple geodesics from a variety of initial conditions (2D)

These utilities are compatible with the symbolic tools thanks to sympy.lambdify, which is used to convert symbolic equations into numeric equations.

*Note that the numeric tools in pystein are still in beta.