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On the Definition of Averagely Trapped Surfaces

Previously suggested definitions of averagely trapped surfaces are not well-defined properties of 2-surfaces, and can include surfaces in flat space-time. A natural definition of averagely trapped surfaces is that the product of the null expansions be positive on average. A surface is averagely trapped in the latter sense if and only if its area $A$ and Hawking mass $M$ satisfy the isoperimetric inequality $16πM^2 > A$, with similar inequalities existing for other definitions of quasi-local energy.