Algebraic classification of five-dimensional spacetimes using scalar invariants

Abstract

There are a number of algebraic classifications of spacetimes in higher dimensions utilizing alignment theory, bivectors and discriminants. Previous work gave a set of necessary conditions in terms of discriminants for a spacetime to be of a particular algebraic type. We demonstrate the discriminant approach by applying the techniques to the Sorkin-Gross-Perry soliton, the supersymmetric and doubly-spinning black rings and some other higher dimensional spacetimes. We show that even in the case of some very complicated metrics it is possible to compute the relevant discriminants and extract useful information from them.

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Cited by in corpus (10)

• Identification of black hole horizons using scalar curvature invariants
• Scalar Polynomial Curvature Invariant Vanishing on the Event Horizon of Any Black Hole Metric Conformal to a Static Spherical Metric
• Petrov Type, Principal Null Directions, and Killing Tensors of Slowly-Rotating Black Holes in Quadratic Gravity
• The complex Goldberg-Sachs theorem in higher dimensions
• The Cartan Algorithm in Five Dimensions
• Refinements of the Weyl tensor classification in five dimensions
• Geometric Horizons in the Kastor-Traschen Multi Black Hole Solutions
• Curvature invariant characterization of event horizons of four-dimensional black holes conformal to stationary black holes
• Horizon Detection and Higher Dimensional Black Rings
• D-dimensional metrics with D-3 symmetries