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Integrability of Five Dimensional Minimal Supergravity and Charged Rotating Black Holes | | Pau Figueras
; Ella Jamsin
; Jorge V. Rocha
; Amitabh Virmani
; | | Date: |
16 Dec 2009 | | Abstract: | We explore the integrability of five-dimensional minimal supergravity in the
presence of three commuting Killing vectors. We argue that to see the
integrability structure of the theory one necessarily has to perform an Ehlers
reduction to two dimensions. A direct dimensional reduction to two dimensions
does not allow us to see the integrability of the theory in an easy way. This
situation is in contrast with vacuum five-dimensional gravity. We derive the
Belinski-Zakharov (BZ) Lax pair for minimal supergravity based on a symmetric
7x7 coset representative matrix for the coset G2/(SL(2,R) x SL(2,R)). We
elucidate the relationship between our BZ Lax pair and the group theoretic Lax
pair previously known in the literature. The BZ Lax pair allows us to
generalize the well-known BZ dressing method to five-dimensional minimal
supergravity. We show that the action of the three-dimensional hidden symmetry
transformations on the BZ dressing method is simply the group action on the BZ
vectors. As an illustration of our formalism, we obtain the doubly spinning
five-dimensional Myers-Perry black hole by applying solitonic transformations
on the Schwarzschild black hole. We also derive the Cvetic-Youm black hole by
applying solitonic transformations on the Reissner-Nordstrom black hole. | | Source: | arXiv, 0912.3199 | | Services: | Forum | Review | PDF | Favorites | |
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