  We extend the conjectured Kerr/CFT correspondence to the case of extremal
Kerr black holes immersed by an magnetic field, namely the extremal Melvin-Kerr
black holes. We compute the central charge which appears in the associated
Virasoro algebra generated by a class of diffeomorphisms that satisfies a set
of boundary conditions in the near horizon of an extremal Melvin-Kerr black
hole. Our results support the Kerr/CFT conjecture, where the macroscopic
Bekenstein-Hawking entropy for an extremal Melvin-Kerr black hole matches the
result obtained from a dual 2D CFT microscopic computation using Cardy formula.
Interestingly, the dual CFT description could be non-unitary, due to the
possibility of negative central charge.
