Run the following code to initialize $\LaTeX$ output and load (Tevian's frontend to) the differential forms package, either by clicking on "Evaluate" or by typing Shift+Enter.
Now enter a line element in the box below, adapting the given code as
needed. First declare any parameters or functions, then provide a list of
coordinates using the MakeC
command as shown below (note the
double parentheses). Finally, set the (covariant) metric to the (inverse of
the) matrix relating the coordinate and orthonormal 1-form bases. The
result should be the line element in tensor notation.
List the nonzero components of the (covariant) metric tensor (in a coordinate basis!).
List the nonzero Christoffel symbols (in an orthonormal frame).
Compute and display the components of the Ricci tensor $R_{ij}$. The Kerr geometry is a vacuum solution of Einstein's equation!
Enter any further code you wish below.
Compute the components $R^i{}_{jkl}$ of the (Riemann) curvature tensor (in an orthonormal frame), but only print a single component.