The hyperbolic Penrose inequality is a mass-area comparison for initial data approaching a hyperbolic reference metric at infinity. In the time-symmetric formulation with
three-dimensional spherical infinity and cosmological constant 
, the scalar curvature
is at least 
and the inner boundary is minimal
and outer area minimizing. The proposed bound is
 |
where 
and 
counts all components of full enclosing cuts. The mass is the Lorentz norm of the
four hyperbolic metric fluxes, 
, assumed future timelike.
These spatial fluxes are metric charges rather than ADM momentum.
