We present two new classes of dyonic anti--de Sitter black hole solutions of four-dimensional maximal N=8, SO(8) gauged supergravity. They are (1) static black holes of N=2, U(1)⁴ gauged supergravity with four electric and four magnetic charges, with spherical, planar or hyperbolic horizons; and (2) rotating black holes of N=2, 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 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.
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Chow et al. (2014) studied this question.
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