# Black holes, hidden symmetries, and complete integrability

@article{Frolov2017BlackHH, title={Black holes, hidden symmetries, and complete integrability}, author={Valeri P. Frolov and Pavel Krtou{\vs} and David Kubizň{\'a}k}, journal={Living Reviews in Relativity}, year={2017}, volume={20} }

The study of higher-dimensional black holes is a subject which has recently attracted 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…

## 154 Citations

### Slowly rotating black holes with exact Killing tensor symmetries

- PhysicsPhysical Review D
- 2022

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…

### Hidden conformal symmetries from Killing towers with an application to large-D/CFT

- PhysicsSciPost Physics
- 2022

We generalize the notion of hidden conformal symmetry in Kerr/CFT to Kerr-(A)dS black holes in arbitrary dimensions.
We build the SL(2, R) generators directly from the Killing tower, whose Killing…

### Hidden symmetries from distortions of the conformal structure

- MathematicsPhysical Review D
- 2022

It is well established that the mass parameter breaks the conformal symmetries in the case of geodesic motion. The proper conformal Killing vectors cease to generate conserved charges when non-null…

### Principal tensor strikes again: Separability of vector equations with torsion

- PhysicsPhysics Letters B
- 2019

### IDEAL characterization of higher dimensional spherically symmetric black holes

- MathematicsClassical and Quantum Gravity
- 2019

In general relativity, an IDEAL (intrinsic, deductive, explicit, algorithmic) characterization of a reference spacetime metric g0 consists of a set of tensorial equations T[g] = 0, constructed…

### Chiral anomalies in black hole spacetimes

- Physics
- 2022

We study the properties of chiral anomalies in a wide class of spacetimes which possess a principal Killing–Yano tensor. This class includes metrics of charged rotating black holes as a special…

### Hidden Conformal Symmetry in Higher Derivative Dynamics for the Kerr Black Hole

- PhysicsUniverse
- 2022

The Kerr/CFT correspondence provides a holographic description of spinning black holes that exist in our universe and the notion of hidden conformal symmetry allows for a formulation of this…

### Integrable systems connected with black holes

- PhysicsCommunications of the Byurakan Astrophysical Observatory
- 2019

We studied some important questions in general relativity and mathematical physics mainly related to the two most important solutions of the theory of relativity - gravitational waves and black…

### Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

- Mathematics
- 2018

We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is…

### Linear Stability of Black Holes and Naked Singularities

- PhysicsUniverse
- 2022

A review of the current status of the linear stability of black holes and naked singularities is given. The standard modal approach, that takes advantage of the background symmetries and analyze…

## References

SHOWING 1-10 OF 433 REFERENCES

### Higher-dimensional black holes: hidden symmetries and separation of variables

- Physics
- 2008

In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and…

### Black Holes, Hidden Symmetry and Complete Integrability: Brief Review

- Physics
- 2012

This chapter contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are…

### Hidden Symmetries of Higher-Dimensional Black Hole Spacetimes(VIII Asia-Pacific International Conference on Gravitation and Astrophysics (ICGA8))

- Physics
- 2007

The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed…

### Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime

- Mathematics, Physics
- 2008

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the…

### Separability of black holes in string theory

- Physics
- 2012

A bstractWe analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We…

### Generalized hidden symmetries and the Kerr-Sen black hole

- Physics
- 2010

We elaborate on basic properties of generalized Killing-Yano tensors which naturally extend Killing-Yano symmetry in the presence of skew-symmetric torsion. In particular, we discuss their…

### Separability in cohomogeneity-2 Kerr-NUT-AdS metrics

- Mathematics
- 2006

The remarkable and unexpected separability of the Hamilton-Jacobi and Klein-Gordon equations in the background of a rotating four-dimensional black hole played an important role in the construction…

### SUPERSYMMETRIC ROTATING BLACK HOLES AND CAUSALITY VIOLATION

- Physics
- 1999

The geodesics of the rotating extreme black hole in five spacetime dimensions found by Breckenridge, Myers, Peet and Vafa are Liouville integrable and may be integrated by additively separating the…