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.
Black holes, hidden symmetries, and complete integrability
10 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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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.
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.
citing papers explorer
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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.
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From (Hidden) Symmetries to Stealth Solutions
Killing-Yano tensors generate p-form stealth solutions in a bumblebee-type Proca theory with fine-tuned curvature terms on arbitrary backgrounds.
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Proca-type Hair of Rotating Black Holes in Higher Dimensions
Spacetime symmetries generate stealth Proca vector fields on arbitrary backgrounds, enabling exact Proca-haired rotating black holes in all dimensions.
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Chaotic behaviors of particles around the black hole with an anisotropic matter immersed in a magnetic field
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).
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The Role of the Volume in Black Hole Thermodynamics
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.
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Light Deflection due to Spinoptic Effects in Parametrized and Spherically Symmetric Hairy Black Holes
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.
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Love numbers of black holes and compact objects
A pedagogical review of Love numbers and tidal responses for black holes and compact objects in general relativity and extensions.
- Anisotropic drag force in finite-density QGP from charged rotating 5D black holes