We present two new classes of dyonic anti–de Sitter black hole solutions of four-dimensional maximal $\mathcal{N}=8$, SO(8) gauged supergravity. They are (1) static black holes of $\mathcal{N}=2$, $\mathrm{U}(1{)}^4$ gauged supergravity with four electric and four magnetic charges, with spherical, planar or hyperbolic horizons; and (2) rotating black holes of $\mathcal{N}=2$, $\mathrm{U}(1{)}^2$ gauged supergravity with two electric and two magnetic charges. We study their thermodynamics, and point out that the formulation of a consistent thermodynamics for dyonic anti–de Sitter black holes is dependent on the existence of boundary conditions for the gauge fields. We identify several distinct classes of boundary conditions for gauge fields in $\mathrm{U}(1{)}^4$ supergravity. We study a general family of metrics containing the rotating solutions, and find Killing-Yano tensors with torsion in two conformal frames, which underlie separability.

• Received 18 November 2013

DOI:https://doi.org/10.1103/PhysRevD.89.065003