Harrison transformation and charged black objects in Kaluza-Klein theory

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.

Thermodynamics of nonextremal Kaluza-Klein multiblack holes in five dimensions

“…Using the Mann-Marolf counterterm to regularize the gravitational action, I 0 will correspond to the action computed on the boundary when taking this counterterm into account. In general dimensions, for spaces with Kaluza-Klein asymptotics we follow the general results from [51]. Assuming one extra-direction (along χ with the length at infinity L) one finds the total mass, gravitational tension, respectively the total action (in absence of conical singularities) to be:…”

“…Finally, in Section 4 we discussed the particular case of N charged KK black holes having fixed mass-to-charge ratio. To generate such a solution from the uncharged version we made use of a charging technique previously discussed in [50,51].…”

“…Such a solution can be easily obtained from the uncharged version presented in the previous section by applying a charging technique. One particularly simple charging technique has been described in [50,51].…”

“…Defining now r ∞ = c √ 1 + c 2 N i=1 (2σ i ) the asymptotic length of the χ-circle becomes L = 4πr ∞ . Using the counterterm approach [52,51] one is now ready to compute the total mass, the gravitational tension and the total electric charge for this configuration:…”

A black ring on the Taub-bolt instanton in five dimensions

“…Since the asymptotic region is the same with that of the Kaluza-Klein magnetic monopole, to compute the conserved charges the easiest way is to use the counter-terms method, as described for instance in [72] or [73]. One obtains the conserved mass M and the gravitational tension T in the form:…”