Kerr Geometry

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 coordinate 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.