Non-extremal Charged Rotating Black Holes in Seven-Dimensional Gauged Supergravity

TL;DR

The paper constructs non-extremal, two-charge rotating black holes in seven-dimensional gauged supergravity with equal angular momenta, revealing that the 4-form field $F_{(4)}$ must satisfy the first-order odd-dimensional self-duality equation $(X_1\, X_2)^2\,{*F_{(4)}} = -2 g\, A_{(3)} - F_{(3)}$, which introduces novel linear-in-$g$ structure absent in lower dimensions. Starting from the ungauged solution via a solution-generating procedure, the authors then propose and verify a gauged generalization, obtaining explicit metrics and gauge fields with detailed dependence on harmonic functions $H_i$, and functions $f_1$, $f_2$, and $Y$ in the full solution; the equal-charge case yields a simpler form. The supersymmetric (BPS) limit is analyzed, yielding the condition $\tanh\delta = \pm 1/(1+ a g)$ for preserved Killing spinors, with further notes on reduced supersymmetry and potential naked CTCs in certain regimes. These results advance the AdS$_7$/CFT$_6$ program in M-theory and highlight the distinctive features introduced by the odd-dimensional self-duality constraint in seven dimensions.

Abstract

We obtain the solution for non-extremal charged rotating black holes in seven-dimensional gauged supergravity, in the case where the three rotation parameters are set equal. There are two independent charges, corresponding to gauge fields in the U(1)xU(1) abelian subgroup of the SO(5) gauge group. A new feature in these solutions, not seen previously in lower-dimensional examples, is that the first-order "odd-dimensional self-duality" equation for the 4-form field strength plays a non-trivial role. We also study the BPS limit of our solutions where the black holes become supersymmetric. Our results are of significance for the AdS_7/CFT_6 correspondence in M-theory.