Slowly rotating black holes with exact Killing tensor symmetries

Abstract

We present a novel family of slowly rotating black hole solutions in four, and higher dimensions, that extend the well known Lense-Thirring spacetime and solve the field equations to linear order in rotation parameter. As "exact metrics" in their own right, the new (non-vacuum) spacetimes feature the following two remarkable properties: i) near the black hole horizon they can be cast in the, manifestly regular, Painlevé-Gullstrand form and ii) they admit exact Killing tensor symmetries. We show these symmetries are inherited from the principal Killing-Yano tensor of the exact rotating black hole geometry in the slow rotation limit. This provides a missing link as to how the exact hidden symmetries emerge as rotation is switched on. Remarkably, in higher dimensions the novel generalized Lense-Thirring spacetimes feature a rapidly growing number of exact irreducible rank-2, as well as higher-rank, Killing tensors -- giving a first example of a physical spacetime with more hidden than explicit symmetries.

7 pages, no figures, v3: minor changes

References in corpus (5)

• Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
• `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
• Spacetime Encodings II - Pictures of Integrability
• Killing tensor and Carter constant for Painleve-Gullstrand form of Lense-Thirring spacetime
• Ricci-flat spacetimes admitting higher rank Killing tensors

Cited by in corpus (5)

• Generalized Lense--Thirring metrics: higher-curvature corrections and solutions with matter
• Love symmetry in higher-dimensional rotating black hole spacetimes
• Killing tensors of generalized Lense-Thirring space-time
• Superradiant instability in slowly rotating Kerr-Newman black holes
• On a lower-dimensional Killing vector origin of irreducible Killing tensors