Curvature Invariants for Rotating and Charged Black Holes (original) (raw)

Riemann curvature invariants are important in general relativity because they encode the geometrical properties of spacetime in a manifestly coordinate-invariant way. Fourteen such invariants are required to characterize four-dimensional spacetime in general, and Zakhary and McIntosh have shown that as many as seventeen can be required in certain degenerate cases. We calculate explicit expressions for all seventeen of these Zakhary-McIntosh curvature invariants for the Kerr-Newman metric that describes spacetime around black holes of the most general kind (those with mass, charge and spin). The resulting plots show a richer and more complex structure than is suggested by traditional (coordinate-dependent) textbook depictions, and may reward further investigation.