Spacetime invariants and their uses

Abstract

There are various types of global and local spacetime invariant in general relativity. Here I focus on the local invariants obtainable from the curvature tensor and its derivatives. The number of such invariants at each order of differentiation that are algebraically independent will be discussed. There is no universally valid choice of a minimal set. The number in a complete set will also be discussed. The invariants can then be used to characterize solutions of the Einstein equations (locally), to test apparently distinct solutions for equivalence, and to construct solutions. Other applications concern limits of families of spacetimes, and the characterization of horizons and singularities. Further uses are briefly mentioned.

Talk given at the International Conference on Relativistic Astrophysics, Lahore, February 2015. To appear in the proceedings, to be published by Punjab University Press

References in corpus (5)

• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• $\mathcal{I}$-degenerate pseudo-Riemannian metrics
• Karlhede's invariant and the black hole firewall proposal
• Parallel Symbolic Computation of Curvature Invariants in General Relativity
• Curvature invariants in algebraically special spacetimes

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• Thermodynamics of Shearing Massless Scalar Field Spacetimes is Inconsistent With the Weyl Curvature Hypothesis
• Cartan Invariants and Event Horizon Detection, Extended Version
• On scalar curvature invariants in three dimensional spacetimes
• Curvature Invariants for Wormholes and Warped Spacetimes
• Dimension of the isometry group in spacetimes with an invariant frame
• Scalar Polynomial Curvature Invariants in the Context of the Cartan-Karlhede Algorithm