Differential Invariants of the Kerr Vacuum

Abstract

The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate and naked cases. These results extend directly to the Kerr-Newman geometry.

arXiv comment12 pages 8 figures. Much more information at http://grtensor.org/diffweyl/

References in corpus (2)

• Properties of the instantaneous Ergo Surface of a Kerr Black Hole
• Invariants of the Kerr Vacuum

Cited by in corpus (8)

• Classes of Exact Solutions to the Teukolsky Master Equation
• Invariant characterization of the Kerr spacetime: Locating the horizon and measuring the mass and spin of rotating black holes using curvature invariants
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• Geometric surfaces: An invariant characterization of spherically symmetric black hole horizons and wormhole throats
• Visualizing Spacetime Curvature via Gradient Flows I: Introduction
• A non-local way around the no-global-symmetries conjecture in quantum gravity?
• A note on a third order curvature invariant in static spacetimes
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities