Harrison transformation and charged black objects in Kaluza-Klein theory

TL;DR

This paper constructs charged black brane solutions in higher-dimensional Kaluza-Klein theory using Harrison transformations, analyzes their thermodynamics, and explores stability and topology-changing transitions, including spinning solutions with nontrivial gyromagnetic ratios.

Contribution

It introduces a method to generate charged black objects in Kaluza-Klein theory via Harrison transformations and extends the quasilocal formalism to compute their charges.

Findings

Charged solutions are thermodynamically unstable in grand canonical ensemble.

Topology-changing transitions are consistent with previous vacuum case scenarios.

Spinning solutions exhibit a gyromagnetic ratio dependent on nonuniformity.

Abstract

We generate charged black brane solutions in $D-$dimensions in a theory of gravity coupled to a dilaton and an antisymmetric form, by using a Harrison-type transformation. The seed vacuum solutions that we use correspond to uplifted Kaluza-Klein black strings and black holes in $(D-p)$-dimensions. A generalization of the Marolf-Mann quasilocal formalism to the Kaluza-Klein theory is also presented, the global charges of the black objects being computed in this way. We argue that the thermodynamics of the charged solutions can be derived from that of the vacuum configurations. Our results show that all charged Kaluza-Klein solutions constructed by means of Harrison transformations are thermodynamically unstable in a grand canonical ensemble. The general formalism is applied to the case of nonuniform black strings and caged black hole solutions in $D=5, 6$ Einstein-Maxwell-dilaton gravity, whose geometrical properties and thermodynamics are discussed. We argue that the topology changing transition scenario, which was previously proposed in the vacuum case, also holds in this case. Spinning generalizations of the charged black strings are constructed in six dimensions in the slowly rotating limit. We find that the gyromagnetic ratio of these solutions possesses a nontrivial dependence on the nonuniformity parameter.