Initialize $\LaTeX$ output and load the Kerr definitions built into Sage. The output should be the line element.
List the nonzero components of the (covariant) metric tensor (in a coordinate basis).
List the nonzero Christoffel symbols (in a coordinate basis).
Compute the components $R^i{}_{jkl}$ of the (Riemann) curvature tensor (in a coordiante basis), but only print a single component.
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.