Metric Module¶
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class
riccipy.metric.Metric¶ Bases:
riccipy.tensor.AbstractTensor,sympy.tensor.tensor.TensorIndexTypeClass representing a tensor that raises and lowers indices.
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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
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einstein¶ G_{munu} = R_{munu} - frac{1}{2} R g_{munu}
Type: Returns the Einstein tensor using the formula
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ricci_scalar¶ R = R^mu_mu
Type: Returns the Ricci scalar using the formula
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ricci_tensor¶ R_{munu} = R^sigma_{musigmanu}
Type: Returns the Ricci tensor using the formula
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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
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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
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class
riccipy.metric.SpacetimeMetric¶ Bases:
riccipy.metric.MetricClass representing psuedo-Riemannian metrics.