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Riemannian Penrose inequality
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Riemannian Penrose inequality
In mathematical
general relativity
, the
Penrose inequality
, first conjectured by Sir
Roger Penrose
, estimates the mass of a
spacetime
in terms of the total area of its
black holes
and is a generalization of the
positive mass theorem
. The
Riemannian Penrose inequality
is an important special case. Specifically, if (
M
,
g
) is an
asymptotically flat
Riemannian
3-manifold
with nonnegative
scalar curvature
and
ADM mass
m
, and
A
is the area of the outermost
minimal surface
(possibly with multiple
connected components
), then the Riemannian Penrose inequality asserts
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