An intrinsic characterization of the Kerr metric

Abstract

We give the necessary and sufficient (local) conditions for a metric tensor to be the Kerr solution. These conditions exclusively involve explicit concomitants of the Riemann tensor.

15 pages; v2: necessary conditions added to theorems 1 and 2, other minor changes

References in corpus (4)

• Uniqueness results for ill posed characteristic problems in curved space-times
• On the invariant symmetries of the $\mathcal{D}$-metrics
• Kerr Initial data
• Rainich theory for type D aligned Einstein-Maxwell solutions

Cited by in corpus (9)

• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• On the construction of a geometric invariant measuring the deviation from Kerr data
• Non-commutative Geometry from Perturbative Quantum Gravity
• Excised black hole spacetimes: quasi-local horizon formalism applied to the Kerr example
• A set of invariant quality factors measuring the deviation from the Kerr metric
• Labeling spherically symmetric spacetimes with the Ricci tensor
• Conserved quantities and integrability for massless spinning particles in general relativity
• An alternative to the Simon tensor
• Spatially-Homogeneous Cosmologies