JHEP, 03, 226 (2021)

A Correspondence between Ricci-flat Kerr and Kaluza-Klein AdS Black Hole

Liang Ma and Hong Lü

 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.

* liangma@tju.edu.cn, mrhonglu@gmail.com

Abstract

We establish an explicit correspondence of Einstein gravity on the squashed spheres that are the U(1) bundles over ℂℙm to the Kaluza-Klein AdS gravity on the tori. This allows us to map the Ricci-flat Kerr metrics in odd dimensions with all equal angular momenta to charged Kaluza-Klein AdS black holes that can be lifted to become singly rotating M-branes and D3-branes. Furthermore, we find maps between Ricci-flat gravitational instantons to the AdS domain walls. In particular the supersymmetric bolt instantons correspond to domain walls that can be interpreted as distributed M-branes and D3-branes, whilst the non-supersymmetric Taub-NUT solutions yield new domain walls that can be lifted to become solutions in M-theory or type IIB supergravity. The correspondence also inspires us to obtain a new superpotential in the Kaluza-Klein AdS gravity in four dimensions.