Visualizing Spacetime Curvature via Gradient Flows III: The Kerr Metric and the Transitional Values of the Spin Parameter

Abstract

The Kerr metric is one of the most important solutions to Einstein's field equations, describing the gravitational field outside a rotating black hole. We thoroughly analyze the curvature scalar invariants to study the Kerr spacetime by examining and visualizing their covariant gradient fields. We discover that the part of the Kerr geometry outside the black hole horizon changes qualitatively depending on the spin parameter, a fact previously unknown. The number of observable critical points of the curvature invariants' gradient fields along the axis of rotation changes at several transitional values of the spin parameter. These transitional values are a fundamental property of the Kerr metric. They are physically important since in general relativity these curvature invariants represent the cumulative tidal and frame-dragging effects of rotating black holes in an observer-independent way.

5 pages, 3 figures, twocolumn revtex 4-1. One figure updated. Final form to appear in Phys Rev D

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Cited by 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
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• Are Black Holes Springy?
• On geometry of deformed black holes: I. Majumdar-Papapetrou binary
• Two discs and a missing triangle: the maximally extended Kerr black hole revisited