The spacetime Penrose inequality and enclosing area
We prove the sharp spacetime Penrose inequality for smooth one-ended initial-data exteriors in every spatial dimension n ≥ 3, under the dominant energy condition, weak future trapping, the stated differentiated decay and positive enclosing area. These hypotheses force the ADM energy-momentum to be future timelike. Area is the infimum over full enclosing cuts in the original metric. In dimensions three and four, two metric derivatives and one tensor derivative suffice, and both positive enclosing area and future timelikeness follow from the hypotheses.
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