Slowly rotating black holes with exact Killing tensor symmetries
arXiv:2110.14671 · doi:10.1103/PhysRevD.105.064017
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.
arXiv comment7 pages, no figures, v3: minor changes
References in corpus (17)
- P-V criticality of charged AdS black holes
- Rotation and the AdS/CFT correspondence
- General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
- Rotating Black Holes in Higher Dimensions with a Cosmological Constant
- Regular coordinate systems for Schwarzschild and other spherical spacetimes
- Black holes, hidden symmetries, and complete integrability
- Particle and light motion in a space-time of a five-dimensional rotating black hole
- Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Superradiance -- the 2020 Edition
- Some Spacetimes with Higher Rank Killing-Stackel Tensors
- Spacetime Encodings II - Pictures of Integrability
- Symmetries of supergravity black holes
- Killing tensor and Carter constant for Painleve-Gullstrand form of Lense-Thirring spacetime
- On Kerr black hole deformations admitting a Carter constant and an invariant criterion for the separability of the wave equation
- Ricci-flat spacetimes admitting higher rank Killing tensors
- On integrability of the Killing equation
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- 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