A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
Skenderis,Asymptotically Anti-de Sitter space-times and their stress energy tensor, Int
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abstract
We consider asymtotically anti-de Sitter spacetimes in general dimensions. We review the origin of infrared divergences in the on-shell gravitational action, and the construction of the renormalized on-shell action by the addition of boundary counterterms. In odd dimensions, the renormalized on-shell action is not invariant under bulk diffeomorphisms that yield conformal transformations in the boundary (holographic Weyl anomaly). We obtain formulae for the gravitational stress energy tensor, defined as the metric variation of the renormalized on-shell action, in terms of coefficients in the asymptotic expansion of the metric near infinity. The stress energy tensor transforms anomalously under bulk diffeomorphisms broken by infrared divergences.
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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.
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The Energy-Momentum-News Complex near Future Null Infinity
A Carroll-covariant energy-momentum-news complex at future null infinity yields Ward identities that generalise the Bondi loss equations, with an anomalous Carroll boost.
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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.