cdb.relativity.abstract

Core general relativity package, mainly a library of various standard expressions.

Importing this library will make \partial a partial derivative and will also declare the greek indices to be space-time indices.

\partial{#}::PartialDerivative; {\mu,\nu,\rho,\sigma,\kappa,\gamma,\lambda}::Indices(spacetime, position=fixed);

$\displaystyle{}\text{Attached property PartialDerivative to }\partial{\#}.$

$\displaystyle{}\text{Attached property Indices(position=fixed) to }\left[\mu, \nu, \rho, \sigma, \kappa, \gamma, \lambda\right].$

riemann_from_christoffel(R: Ex, c: Ex) -> Ex

Generates an equality which determines the Riemann tensor in terms of the Christoffel symbols.

Generates an equality which determines the Christoffel symbols in terms of the metric.

Convert contractions of Riemann tensors to Ricci tensors or scalars.

ex:= R^{a}_{b c a} - R^{a}_{b a c};

$\displaystyle{}R^{a}\,_{b c a}-R^{a}\,_{b a c}$

R^{a}_{b c a}-R^{a}_{b a c}

riemann_to_ricci(ex);

$\displaystyle{}-2R_{b c}$

-2R_{b c}