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We construct a covariant phase space for rotating weakly isolated horizons in Einstein-Maxwell-Chern-Simons theory in all (odd) $D\geq5$ dimensions.
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Korzi n ´ \acute{\mbox{n}} ski M, Lewandowski J and Pawlowski T 2005 Mechanics of multidimensional isolated horizons Class. Quantum Grav. 22
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Ashtekar A, Beetle C and Lewandowski J 2002 Geometry of generic isolated horizons Class. Quantum Grav. 19
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