All four-dimensional static, spherically symmetric, two-charge Abelian Kaluza–Klein black holes and their CFT duals

Abstract

We derive the dual conformal field theory Virasoro algebras from the algebra of conserved diffeomorphism charges for a large class of Abelian Kaluza–Klein black holes. Under certain conditions, such as non-vanishing electric and magnetic monopole charges, the Kaluza–Klein black holes have a Reissner–Nordstrom spacetime structure. For the non-extremal charged Kaluza–Klein black holes, we use the uplifted 6D pure gravity solutions to construct a set of Killing horizon preserving diffeomorphisms. For the (non-supersymmetric) extremal black holes, we take the near-extremal near-horizon (NENH) limit and construct a one-parameter family of diffeomorphisms which preserve the Hamiltonian constraints at spatial infinity. In each case we evaluate the algebra of conserved diffeomorphism charges following Barnich, Brandt and Compère, who used a cohomological approach, and Silva, who employed a covariant-Lagrangian formalism. At the Killing horizon, it is only Silva's algebra which acquires a central charge extension and which enables us to recover the Bekenstein–Hawking black hole entropy from the Cardy formula. For the NENH geometry, the extremal black hole entropy is obtained only when the free parameter of the diffeomorphism-generating vector fields is chosen such that the central terms of the two algebras are in agreement.