Vanishing scalar invariant spacetime

In mathematical physics, vanishing scalar invariant (VSI) spacetimes are Lorentzian manifolds with all polynomial curvature invariants of all orders vanishing. Although the only Riemannian manifold with VSI property is flat space, the Lorentzian case admits nontrivial spacetimes with this property. Distinguishing these VSI spacetimes from Minkowski spacetime requires comparing non-polynomial invariants[1] or carrying out the full Cartan–Karlhede algorithm on non-scalar quantities.[2][3]

All VSI spacetimes are Kundt spacetimes.[4] An example with this property in four dimensions is a pp-wave. VSI spacetimes however also contain some other four-dimensional Kundt spacetimes of Petrov type N and III. VSI spacetimes in higher dimensions have similar properties as in the four-dimensional case.[5][6]

References

  1. ↑ Page, Don N. (2009), "Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing", Classical Quantum Gravity, 26: 055016, arXiv:0806.2144 Freely accessible, doi:10.1088/0264-9381/26/5/055016
  2. ↑ Koutras, A. (1992), "A spacetime for which the Karlhede invariant classification requires the fourth covariant derivative of the Riemann tensor", Classical Quantum Gravity, 9: L143, doi:10.1088/0264-9381/9/10/003
  3. ↑ Koutras, A.; McIntosh, C. (1996), "A metric with no symmetries or invariants", Classical Quantum Gravity, 13: L47, doi:10.1088/0264-9381/13/5/002
  4. ↑ Pravda, V.; Pravdova, A.; Coley, A.; Milson, R. (2002), "All spacetimes with vanishing curvature invariants", Classical Quantum Gravity, 19 (23): 6213, arXiv:gr-qc/0209024 Freely accessible, doi:10.1088/0264-9381/19/23/318
  5. ↑ Coley, A.; Milson, R.; Pravda, V.; Pravdova, A. (2004), "Vanishing Scalar Invariant Spacetimes in Higher Dimensions", Classical Quantum Gravity, 21: 5519, arXiv:gr-qc/0410070 Freely accessible, doi:10.1088/0264-9381/21/23/014.
  6. ↑ Coley, A.; Fuster, A.; Hervik, S.; Pelavas, N. (2006), "Higher dimensional VSI spacetimes", Classical Quantum Gravity, 23: 7431, arXiv:gr-qc/0611019 Freely accessible, doi:10.1088/0264-9381/23/24/014


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