Run the following code to initialize $\LaTeX$ output and load some macros, 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, enter the components $s^i{}_j$ of an
orthonormal basis $\{\sigma^i\}$ of 1-forms with respect to a coordinate
basis $dx^j$ (so that $\sigma^i=s^i{}_j\,dx^j$), and run
the `MakeS`

command (whose first argument is the signature). 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.
(You can convert the answer to a coordinate basis with the
command `nab.display(f)`

.)

(This computation can take several minutes.)

Compute and display the components of the Ricci tensor $R_{ij}$.
The Kerr geometry is a vacuum solution of Einstein's equation!

(This computation can take several minutes.)

Compute and display the components of the Einstein tensor $G_{ij}$.

Enter any further code you wish below.