Sasaki-Einstein Twist of Kerr-AdS Black Holes

We present Kerr-AdS black holes with equal angular momenta in arbitrary odd spacetime dimensions ≥ 5. The solutions include three non-trivial parameters, mass, angular momentum and an additional parameter δ. For a special value of δ, by twisting the Killing vector fields of the black holes, we reproduce the compact Sasaki-Einstein manifolds constructed by Gauntlett, Martelli, Sparks and Waldram. We also discuss an implication of the twist in string theory and M-theory. [email protected] [email protected] [email protected] 1 Kerr-AdS black holes are characterized by mass, angular momenta and cosmological constant. In spacetime dimension d, the number of angular momenta is equal to the rank of the rotation group SO(d − 1). The five-dimensional Kerr-AdS black holes with two angular momenta were constructed in [1], and recently the general form in arbitrary dimension was found by using the Kerr-Schild ansatz [2]. On the other hand, the Wick rotation of the black holes leads to Riemannian metrics. However, the metrics in general do not extend smoothly to compact manifolds. In [3][4][2], it was shown that this can be achieved by taking a certain limit (Page limit) which enhances the isometry of the metric. Indeed, the infinite series of Einstein metrics on compact manifolds were explicitly constructed [4][2], and analyzed in detail in [5]. Recently, infinite series of Sasaki-Einstein metrics on compact manifolds were presented in [6][7]. It is expected that these metrics can be related to some Kerr-AdS black holes by a certain limit. Our aim in this paper is to clarify the relation between them. We will present (2n+ 3)-dimensional Kerr-AdS black holes with an additional parameter and to derive the Sasaki-Einstein metrics by twisting the two Killing vector fields of the black holes. We find the (2n + 3)-dimensional Kerr-AdS black hole with a negative cosmological constant (2n + 2)λ < 0 (n ≥ 1) as follows: ĝ = − (r) b̂(r) dt + dr Ŵ (r) + r (