= Riemannian Penrose inequality
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{title2=$m_{\rm ADM}\geq\sqrt{A/(16\pi)}$}
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For complete asymptotically flat three-dimensional Riemannian initial data with nonnegative <scalar curvature> and an outermost compact <minimal surface> boundary of area $A$, the <Riemannian Penrose inequality> gives the displayed bound. Equality is realized by the spatial exterior of <Schwarzschild spacetime>. Time-symmetric gravitational initial data have this form when the <Einstein field equations> and energy hypothesis give the required nonnegative curvature. This theorem does not justify substituting arbitrary non-time-symmetric <apparent horizon> area into the same formula.
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