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.