Positivity of a weighted holographic energy is proven for 4D spacetimes with negative cosmological constant and conformally static boundaries of spherical or toroidal topology with compatible spin structure.
Chruściel,On the Relation Between the Einstein and the Komar Expressions for the Energy of the Grav- itational Field, Ann
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Positivity of holographic energy
Positivity of a weighted holographic energy is proven for 4D spacetimes with negative cosmological constant and conformally static boundaries of spherical or toroidal topology with compatible spin structure.