Nonvanishing Local Scalar Invariants even in VSI Spacetimes with all Polynomial Curvature Scalar Invariants Vanishing

Abstract

VSI (`vanishing scalar invariant') spacetimes have zero values for all total scalar contractions of all polynomials in the Riemann tensor and its covariant derivatives. However, there are other ways of concocting local scalar invariants (nonpolynomial) from the Riemann tensor that need not vanish even in VSI spacetimes, such as Cartan invariants. Simple examples are given that reduce to the squared amplitude for a linearized monochromatic plane gravitational wave. These nonpolynomial local scalar invariants are also evaluated for non-VSI spacetimes such as Schwarzschild and Kerr and are estimated near the surface of the earth. Similar invariants are defined for null fluids and for electromagnetic fields.

arXiv comment9 pages, LaTeX, proofread version accepted 2009 January 14 for publication in Classical and Quantum Gravity

References in corpus (12)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• All spacetimes with vanishing curvature invariants
• Vanishing Scalar Invariant Spacetimes in Higher Dimensions
• Alignment and algebraically special tensors in Lorentzian geometry
• Metrics With Vanishing Quantum Corrections
• Higher dimensional VSI spacetimes
• Generalizations of pp-wave spacetimes in higher dimensions
• Curvature invariants in type N spacetimes
• WANDs of the Black Ring
• A Class of Exact Classical Solutions to String Theory
• Vanishing Scalar Invariant Spacetimes in Supergravity
• VSI_i spacetimes and the epsilon-property

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