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Open AccessArticle

Curvature Invariants for Charged and Rotating Black Holes

1
Department of Physics, Astronomy and Geosciences, Towson University, Towson, MD 21252, USA
2
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
3
Department of Physics, University of California, San Diego, CA 92093, USA
*
Author to whom correspondence should be addressed.
Universe 2020, 6(2), 22; https://doi.org/10.3390/universe6020022
Received: 25 October 2019 / Revised: 18 January 2020 / Accepted: 21 January 2020 / Published: 24 January 2020
(This article belongs to the Special Issue Probing New Physics with Black Holes)
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 showed 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), and confirm that they are related by eight algebraic conditions (dubbed syzygies by Zakhary and McIntosh), which serve as a useful check on our results. Plots of these invariants show richer structure than is suggested by traditional (coordinate-dependent) textbook depictions, and may repay further investigation. View Full-Text
Keywords: black holes; curvature invariants; general relativity black holes; curvature invariants; general relativity
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MDPI and ACS Style

Overduin, J.; Coplan, M.; Wilcomb, K.; Henry, R.C. Curvature Invariants for Charged and Rotating Black Holes. Universe 2020, 6, 22.

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