Black hole area–angular-momentum inequality in nonvacuum spacetimes

We show that the area-angular-momentum inequality $A\ge 8\pi |J|$ 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.