Curvature Invariants for Charged and Rotating Black Holes

• DOI: 10.3390/universe6020022
• Publication Date: 2020-01-24T16:01:00Z
• Authors: James Overduin; Max Coplan; Kielan Wilcomb; Richard Conn Henry
• Keywords: Black hole (networking)

Riemann curvature invariants are important in general relativity because they encode the geometrical properties of spacetime a manifestly coordinate-invariant way. Fourteen such required to characterize four-dimensional general, and Zakhary McIntosh showed that as many seventeen can be certain degenerate cases. We calculate explicit expressions for all these Zakhary–McIntosh Kerr–Newman metric describes around black holes most kind (those with mass, charge, spin), confirm related by eight algebraic conditions (dubbed syzygies McIntosh), which serve useful check on our results. Plots show richer structure than is suggested traditional (coordinate-dependent) textbook depictions, may repay further investigation.