Second order scalar invariants of the Riemann tensor: applications to black hole spacetimes

We discuss the Kretschmann, Chern-Pontryagin and Euler invariants among
the second order scalar invariants of the Riemann tensor in any spacetime
in the Newman-Penrose formalism and in the framework of
gravitoelectromagnetism, using the Kerr-Newman geometry as an example. An
analogy with electromagnetic invariants leads to the definition of regions
of gravitoelectric or gravitomagnetic dominance.