Proves that separability of geodesic motion and parallel transport along geodesics implies separability of the linear-in-spin Hamilton-Jacobi equation for test particles.
Black holes, hidden symmetries, and complete integrability
13 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
The study of higher-dimensional black holes is a subject which has recently attracted a vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional black holes. We start with the overview of the Liouville theory of completely integrable systems and introduce Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a `seed object' which generates all these symmetries. It determines the form of the black hole geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.
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In the rotating García-Díaz NLED black hole the Fresnel quartic factorizes into two optical metrics whose critical families project to distinct contours Γ+ and Γ- whose angular separation is generated by the constitutive response and redistributed by spin.
The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.
Killing-Yano tensors generate p-form stealth solutions in a bumblebee-type Proca theory with fine-tuned curvature terms on arbitrary backgrounds.
Spacetime symmetries generate stealth Proca vector fields on arbitrary backgrounds, enabling exact Proca-haired rotating black holes in all dimensions.
Torsion-modified vector equations separate in the Chong-Cvetič-Lu-Pope black hole via a generalized principal Killing-Yano tensor.
Near-EVH limits of AdS6 and AdS7 black holes produce conformally related lower-dimensional black hole solutions in EMMD gravity, opening a potential path to microscopic entropy counting for non-AdS black holes via higher-dimensional AdS/CFT.
Exact black hole solution with anisotropic matter and magnetic field shows the matter parameter reduces local chaos (Lyapunov exponent) while the magnetic field drives qualitative shifts in global chaos (Poincaré sections).
Adapting Barnich-Compère conserved charges, the first law requires unvarying components for both the Killing vector and AdS background (true for E's ξ but not F's β), while V_C enters the β-Smarr relation due to simplifications from the principal conformal Killing-Yano tensor.
Derives exact integrable non-geodesic trajectories for spinning test particles in global monopole spacetime via MPD equations and symmetries.
Spinoptics calculations show parameter-dependent out-of-plane deflection angles for light in RZ and hairy black hole spacetimes, with assessment of mimicry between the models.
A pedagogical review of Love numbers and tidal responses for black holes and compact objects in general relativity and extensions.
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The Bohlin variant of the Eisenhart lift
The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.