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SECOND ORDER SCALAR INVARIANTS OF THE RIEMANN TENSOR: APPLICATIONS TO BLACK HOLE SPACETIMES

CHRISTIAN CHERUBINIInternational Center for Relativistic Astrophysics, I.C.R.A., University of Rome La Sapienza, I–00185 Roma, ItalyDONATO BINIInternational Center for Relativistic Astrophysics, I.C.R.A., University of Rome La Sapienza, I–00185 Roma, ItalySALVATORE CAPOZZIELLOPhysics Department "E. R. Caianiello", University of Salerno, I–84081, ItalyREMO RUFFINIInternational Center for Relativistic Astrophysics, I.C.R.A., University of Rome La Sapienza, I–00185 Roma, Italy
2002en
ABI

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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.

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