General Relativity, Einstein & All That (GREAT)

First, load the package

<< GREAT.m

Brief on-line help is available for all functions:

?IMetric

A sample calculation

First define the coordinate n-vector:

x = {x0, x1}

and then specify the metric as a square n×n matrix:

(met = {{a[x0], b[x1]}, {b[x1], c[x0]}}) // MatrixForm

"IMetric" is the only 1-argument function:

IMetric[met] // MatrixForm

All other "functions" take two arguments, the metric matrix and then the coordinate vector:

Christoffel[met, x]

Riemann[met, x]

Ricci[met, x]

SCurvature[met, x]

EinsteinTensor[met, x]

SqRicci[met, x]

SqRiemann[met, x]

The above "functions" do perform a Simplify[] on the result, but you may want to further manipulate the expression into something that may be more usable, depending on the particular application.