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We show that the area-angular-momentum inequality A≥8π|J| holds for axially symmetric closed outermost stably marginally trapped surfaces. These are horizon sections (in particular, apparent horizons) contained in otherwise generic non-necessarily axisymmetric black hole spacetimes, with a non-negative cosmological constant and whose matter content satisfies the dominant energy condition.
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Jaramillo et al. (2011) studied this question.
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