Hidden symmetries and Killing spinor of 5-dimensional minimal gauged supergravity solutions

Abstract

We investigate the hidden symmetries and existence of Killing spinors of D=5 minimal gauged supergravity solutions which admit a Killing-Maxwell system in the sense of Carter, such as the Chong-Cveti$\check{c}$-L\"{u}-Pope (CCLP) Kerr-dS black hole spacetime and a 5-dimensional minimal gauged supergravity solution endowed with a Sasaki structure deformed by torsion, a limiting case of the generalization of the 5-dimensional toric Sasaki-Einstein $L^{a,b,c}$ spacetime. We note that when an electromagnetic tensor is present and an associated Killing-Maxwell system can be constructed in the sense of Carter, the Killing-Maxwell field becomes a PCKY (principal conformal Killing-Yano) tensor or a PGCKY (principal generalized conformal Killing-Yano) tensor, the latter in the presence of torsion. We find some new hidden symmetries of the Chong-Cveti$\check{c}$-L\"{u}-Pope black hole, i.e. we construct two more generalized St\"ackel-Killing tensors and the associated generalized Killing-Yano (GKY) tensors. We also explicitly construct a Killing spinor for the specific 5 dimensional minimal gauged supergravity solution that is endowed with a Sasaki structure deformed by torsion mentioned above.