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Mass and Tension (momentum) Sum Rules in AdS (dS)

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The stress-energy tensor in a conformal field theory has
zero trace.

Hence AdS boundary stress-tensors are traceless by
construction, to match this property of the dual CFT. An elegant (aka nifty)
construction based on the conformal isometry of AdS will be presented which
shows that in an asymptotically AdS spacetime, the sum of the ADM mass and the
ADM tensions is zero. This result follows strictly from the gravitational point
of view- that is, the Einstein equations and the definitions of the ADM
charges. Further, it turns out that perturbative stress-energy sources in an asymptotically
AdS spacetime must satisfy a local version of this constraint, namely that the
sum of the energy density minus the pressures equals zero. The situation with
positive cosmological constant is both similar and distinct in interesting
ways, which will be briefly discussed. The analogous (analytically continued)
conformal isometry in dS is the root of the

``k^4 “ power spectrum for causal cosmological
perturbations. Work in progress (speculations) will be presented about a
corresponding sum-rule for gravitational charges defined at future infinity in
a spacetime that approaches dS at late times.