Supersymmetric Black Holes with a Single Axial Symmetry in Five Dimensions

Katona, D.; Lucietti, James

doi:10.1007/s00220-022-04576-7

Cited by 6 publications

(2 citation statements)

References 112 publications

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“…The use of invariant quantities derived from Killing invariants is not restricted to 4D GR or its modifications. For example, the classification of five-dimensional supersymmetric black holes with a single axial symmetry was accomplished using the norm of a Killing vector field as a global invariant for the solutions [22,23]. In gravitational theories involving torsion, such as Einstein-Cartan or teleparallel gravity, a frame formalism can be adapted to the group of symmetries in order to derive the most general family of solutions that admit that symmetry group.…”

Section: Introductionmentioning

confidence: 99%

Killing Invariants: An approach to the sub-classification of geometries with symmetry

Brown,

Gorban,

Julius

et al. 2024

Preprint

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In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes is potentially computationally difficult or not at all possible. This difficulty will arise whenever the classifying invariants are either high-degree rational functions or depend on transcendental functions without standard inverses. In the case that spacetimes admit Killing vectors with non-trivial orbits, we propose a new set of invariant quantities, called Killing invariants. These invariants will allow for the sub-classification of spacetimes admitting the same group of symmetries and will, in principle, be substantially less complicated than any other known set. We apply this approach to the class of static spherically symmetric geometries as an illustrative example.

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Section: Introductionmentioning

confidence: 99%

Killing Invariants: An approach to the sub-classification of geometries with symmetry

Brown,

Gorban,

Julius

et al. 2024

Preprint

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“…The BGPP metric is still of importance due to its role of a seed in the development of geometries in higher dimensions: in [4] Einstein 5D geometries with a negative cosmological constant, in [7] Einstein-Maxwell metrics for D ⩾ 6 and in [14] a supersymmetric black-hole in 5D.…”

Section: Introductionmentioning

confidence: 99%

The geodesic flow of the BGPP metric is Liouville integrable

Maciejewski

Przybylska

Valent³

2023

Class. Quantum Grav.

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We prove that the geodesics equations corresponding to the BGPP metric areintegrable in the Liouville sense. The $\mathrm{SO}(3,\mathbb{R})$ symmetry ofthe model allows to reduce the system from four to two degrees of freedom.Moreover, solutions of the reduced system and its degenerations can be solvedexplicitly or reduced to a certain quadrature. In degenerated cases BGPP metriccoincides with the Eguchi-Hanson metric and for this case the mentionedquadrature can be calculated explicitly in terms of elliptic integrals. 

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A Classification of Supersymmetric Kaluza–Klein Black Holes with a Single Axial Symmetry

Katona

2024

Ann. Henri Poincaré

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We extend the recent classification of five-dimensional, supersymmetric asymptotically flat black holes with only a single axial symmetry to black holes with Kaluza–Klein asymptotics. This includes a similar class of solutions for which the supersymmetric Killing field is generically timelike, and the corresponding base (orbit space of the supersymmetric Killing field) is of multi-centred Gibbons–Hawking type. These solutions are determined by four harmonic functions on $$\mathbb {R}^3$$ R 3 with simple poles at the centres corresponding to connected components of the horizon, and fixed points of the axial symmetry. The allowed horizon topologies are $$S^3$$ S 3 , $$S^2\times S^1$$ S 2 × S 1 , and lens space L(p, 1), and the domain of outer communication may have non-trivial topology with non-contractible 2-cycles. The classification also reveals a novel class of supersymmetric (multi-)black rings for which the supersymmetric Killing field is globally null. These solutions are determined by two harmonic functions on $$\mathbb {R}^3$$ R 3 with simple poles at centres corresponding to horizon components. We determine the subclass of Kaluza–Klein black holes that can be dimensionally reduced to obtain smooth, supersymmetric, four-dimensional multi-black holes. This gives a classification of four-dimensional asymptotically flat supersymmetric multi-black holes first described by Denef et al.

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Supersymmetric Black Holes with a Single Axial Symmetry in Five Dimensions

Cited by 6 publications

References 112 publications

Killing Invariants: An approach to the sub-classification of geometries with symmetry

Killing Invariants: An approach to the sub-classification of geometries with symmetry

The geodesic flow of the BGPP metric is Liouville integrable

A Classification of Supersymmetric Kaluza–Klein Black Holes with a Single Axial Symmetry

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