Thermodynamics of rotating NUTty dyons

Alvaro Ballon Bordo,David Kubizňák,Finnian Gray

doi:10.1007/jhep05(2020)084

Alvaro Ballon Bordo, David Kubizňák + Show 1 more

Open Access

https://doi.org/10.1007/jhep05(2020)084

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Abstract

We extend the work on thermodynamics of Lorentzian NUTty solutions, by including simultaneously the effect of rotation and electromagnetic charges. Due to the fact that Misner strings carry electric charge, and similar to the non-rotating case, we observe an interesting interplay between the horizon and asymptotic charges. Namely, upon employing the Euclidean action calculation we derive two alternative full cohomogeneity first laws, one that includes the variations of the horizon electric charge and the asymptotic magnetic charge and another that involves the horizon magnetic charge and the asymptotic electric charge. When one of the horizon charges vanishes, we obtain the corresponding ‘electric’ and ‘magnetic’ first laws that are connected by the electromagnetic duality. We also briefly study the free energy of the corresponding system.

Highlights

The purpose of this work is to extend the above results and formulate the first law for the rotating NUTty dyons in the asymptotically flat case
We extend the work on thermodynamics of Lorentzian NUTty solutions, by including simultaneously the effect of rotation and electromagnetic charges
In order to write down the first law of thermodynamics for rotating NUTty dyons, we have employed the technique of Euclidean action calculation

Summary

Rotating NUTty dyons

The geometry of a rotating NUTty dyon can be obtained by a certain limit of the general type D Plebanski-Demianski spacetime [29]. The other two are located along the north and south pole axis cos θ = ±1, i.e., along the Misner strings and generated by the Killing vectors ξ± = ∂t + Ω±∂φ. As a string temperature, κ±/(4π), or as angular velocity, |Ω±|/(4π) The latter perspective is argued for in [26] in the context of rotating Taub-NUT thermodynamics, where the Misner charges are interpreted as the string angular momenta (see [22]). Similar to the non-rotating case, we find that Misner strings carry charges and the field strength integral over a 2-sphere depends on the radius. The first step is to find a gauge, by applying A → A + Φet dt, to ensure that the electrostatic potential defined by Φe(r) = −ξaAa vanishes on the horizon, Φe(r+) = 0.

Possibility 1: horizon magnetic charge

Electric and magnetic first laws

Conclusions

A Euclidean action calculation