Charged Rotating Black Holes in Four-Dimensional Gauged and Ungauged Supergravities

TL;DR

The authors develop a robust solution-generating framework for four-dimensional rotating, charged black holes in both ungauged and gauged supergravities by performing a timelike reduction to three dimensions, revealing an $O(4,4)$ global symmetry. They explicitly construct four-charge rotating black holes in ungauged ${ m N}=2$ supergravity (embedded in ${ m N}=8$) and obtain pairwise-equal-charge gauged ${ m N}=4$ solutions, including non-trivial dilaton/axion profiles and uplift to higher dimensions. They also extend these solutions to include NUT and acceleration parameters, and demonstrate the AdS$_4$/CFT$_3$ relevance of the gauged backgrounds at finite temperature. The methods provide explicit, gauge-potential-covered metrics and fields, enabling detailed holographic and microscopic entropy analyses. Overall, the work delivers new exact backgrounds with rich charge and geometric structures for holography and string/M-theory compactifications.

Abstract

We study four-dimensional non-extremal charged rotating black holes in ungauged and gauged supergravity. In the ungauged case, we obtain rotating black holes with four independent charges, as solutions of N=2 supergravity coupled to three abelian vector multiplets. This is done by reducing the theory along the time direction to three dimensions, where it has an O(4,4) global symmetry. Applied to the reduction of the uncharged Kerr metric, O(1,1)^4\subset O(4,4) transformations generate new solutions that correspond, after lifting back to four dimensions, to the introduction of four independent electromagnetic charges. In the case where these charges are set pairwise equal, we then generalise the four-dimensional rotating black holes to solutions of gauged N=4 supergravity, with mass, angular momentum and two independent electromagnetic charges. The dilaton and axion fields are non-constant. We also find generalisations of the gauged and ungauged solutions to include the NUT parameter, and for the ungauged solutions, the acceleration parameter too. The solutions in gauged supergravity provide new gravitational backgrounds for a further study of the AdS_4/CFT_3 correspondence at non-zero temperature.