# On the uniqueness of supersymmetric AdS(5) black holes with toric symmetry

@article{Lucietti2022OnTU, title={On the uniqueness of supersymmetric AdS(5) black holes with toric symmetry}, author={James Lucietti and Praxitelis Ntokos and Sergei G Ovchinnikov}, journal={Classical and Quantum Gravity}, year={2022}, volume={39} }

We consider the classification of supersymmetric AdS5 black hole solutions to minimal gauged supergravity that admit a torus symmetry. This problem reduces to finding a class of toric Kähler metrics on the base space, which in symplectic coordinates are determined by a symplectic potential. We derive the general form of the symplectic potential near any component of the horizon or axis of symmetry, which determines its singular part for any black hole solution in this class, including possible…

## References

SHOWING 1-9 OF 9 REFERENCES

### The Geometry of Weakly Self-dual Kähler Surfaces

- MathematicsCompositio Mathematica
- 2003

We study Kähler surfaces with harmonic anti-self-dual Weyl tensor. We provide an explicit local description, which we use to obtain the complete classification in the compact case. We give new…

### Kaehler structures on toric varieties

- Mathematics
- 1994

1. Let (X, ω) be a compact connected 2w-dimensional manifold, and let (1.1) τ: T -+Όifί(X, ω) be an effective Hamiltonian action of the standard w-torus. Let φ: X —> R be its moment map. The image,…

### Kahler geometry of toric manifolds in symplectic coordinates

- Mathematics
- 2000

A theorem of Delzant states that any symplectic manifold $(M,\om)$ of dimension $2n$, equipped with an effective Hamiltonian action of the standard $n$-torus $\T^n = \R^{n}/2\pi\Z^n$, is a smooth…

### Commun

- Math. Phys. 365
- 2019

### 015 doi:10.1088/1126-6708/2007/12/015 [arXiv:0708.3695 [hep-th]

- Kunduri and J. Lucietti, JHEP
- 2007

### Class

- Quant. Grav. 36
- 2019

### Living Rev

- Rel. 23
- 2020