Metric Module

class riccipy.metric.Metric

Bases: riccipy.tensor.AbstractTensor, sympy.tensor.tensor.TensorIndexType

Class representing a tensor that raises and lowers indices.

christoffel

Gamma^sigma_{munu} = frac{1}{2} g^{sigmarho} (partial_mu g_{nurho} + partial_nu g_{rhomu} - partial_rho g_{munu})

Type:Returns the Christoffel symbols using the formula
einstein

G_{munu} = R_{munu} - frac{1}{2} R g_{munu}

Type:Returns the Einstein tensor using the formula
ricci_scalar

R = R^mu_mu

Type:Returns the Ricci scalar using the formula
ricci_tensor

R_{munu} = R^sigma_{musigmanu}

Type:Returns the Ricci tensor using the formula
riemann

R^rho_{sigmamunu} = partial_mu Gamma^rho_{nusigma} - partial_nu Gamma^rho_{musigma} + Gamma^rho_{mulambda} Gamma^lambda_{nusigma} - Gamma^rho_{nulambda} Gamma^lambda_{musigma}

Type:Returns the Riemann curvature tensor using the formula
weyl

C_{rhosigmamunu} = R_{rhosigmamunu} - frac{2}{(n - 2)} (g_{rho[mu} R_{nu]sigma} - g_{sigma[mu} R_{nu]rho}) + frac{2}{(n - 1)(n - 2)} g_{rho[mu} g_{nu]sigma} R

Type:Returns the Weyl conformal tensor using the formula
class riccipy.metric.SpacetimeMetric

Bases: riccipy.metric.Metric

Class representing psuedo-Riemannian metrics.