All 4-dimensional static, spherically symmetric, 2-charge abelian Kaluza-Klein black holes and their CFT duals

TL;DR

This paper derives the dual CFT Virasoro algebras for a broad class of 4D abelian Kaluza-Klein black holes, connecting their horizon symmetries to black hole entropy via the Cardy formula, using covariant charge methods.

Contribution

It constructs horizon-preserving diffeomorphisms for non-extremal and extremal Kaluza-Klein black holes and evaluates their conserved charge algebras, revealing the central charge extension necessary for entropy calculation.

Findings

Virasoro algebra with central charge is obtained at the horizon.

Black hole entropy matches the Cardy formula when central charges are correctly identified.

Different algebraic approaches yield consistent entropy results for Kaluza-Klein black holes.

Abstract

We derive the dual CFT 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 space-time 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 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 Compere, 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.