The volume-renormalized mass of an asymptotically hyperbolic initial data set equals a Fischer-Moncrief-style reduced Hamiltonian for asymptotically Milne-like spacetimes and is monotone under Einstein evolution.
Gourgoulhon.3+ 1 formalism in general relativity: bases of numerical relativity, volume 846
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The Volume-Renormalized Mass from a Hamiltonian Perspective
The volume-renormalized mass of an asymptotically hyperbolic initial data set equals a Fischer-Moncrief-style reduced Hamiltonian for asymptotically Milne-like spacetimes and is monotone under Einstein evolution.