Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution

Abstract

We explore various aspects of the self-dual Plebański-Demiański family in the Euclidean Einstein-Maxwell-$\Lambda$ system. The Killing-Yano tensor which was recently found by Yasui and one of the present authors allows us to prove that the self-dual Plebański-Demiański metric can be brought into the self-dual Carter metric by an orientation-reversing coordinate transformation. We show that the self-dual Plebański-Demiański solution admits two independent Killing spinors in the framework of $N=2$ minimal gauged supergravity, whereas the non-self-dual solution admits only a single Killing spinor. This can be demonstrated by casting the self-dual Plebański-Demiański metric into two distinct Przanowski-Tod forms. As a by-product, a new example of the three-dimensional Einstein-Weyl space is presented. We also prove that the self-dual Plebański-Demiański metric falls into two different Calderbank-Pedersen families, which are determined by a single function subjected to a linear equation on the two dimensional hyperbolic space. Furthermore, we consider the hyper-Kähler case for which the metric falls into the Gibbons-Hawking class. We find that the condition for the nonexistence of Dirac-Misner string enforces the solution with a nonvanishing acceleration parameter to the Eguchi-Hanson space.

41 pages, v3: minor modifications, refs added, published version in CQG

References in corpus (20)

• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
• On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
• Einstein-Maxwell gravitational instantons and five dimensional solitonic strings
• Killing(-Yano) Tensors in String Theory
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality
• Killing-Yano equations and G-structures
• The Disjointed Thermodynamics of Rotating Black Holes With a NUT Twist
• Geometry of Killing spinors in neutral signature
• Quasinormal modes of black holes localized on the Randall-Sundrum 2-brane
• Cosmological rotating black holes in five-dimensional fake supergravity
• A simple test for spacetime symmetry
• A Note on Riemannian Anti-self-dual Einstein metrics with Symmetry
• Localization principle in SUSY gauge theories
• Quaternion-Kaehler four-manifolds and Przanowski's function
• A Class of Integrable Metrics
• Killing 2-forms in dimension 4
• Rotating black holes in an expanding universe from fake supergravity
• A Class of Integrable Metrics II

Cited by in corpus (9)

• Partition functions on 3d circle bundles and their gravity duals
• New family of C-metrics in $\mathcal{N}=2$ gauged supergravity
• Conformal invariance, complex structures, and the Teukolsky connection
• Wormhole $C$ metric
• Euclidean supersymmetric solutions with the self-dual Weyl tensor
• An alternative to the Simon tensor
• Supersymmetry of the Robinson-Trautman solution
• Kerr metric from two commuting complex structures
• Kerr-Schild transformation of the Benenti-Francaviglia metric