PIRSA:12110042 Scientific Series Quantum Gravity

DOI10.48660/12110042

Series: Cosmology and Gravitation

Traschen, J. (2012). Mass and Tension (momentum) Sum Rules in AdS (dS). Perimeter Institute. https://pirsa.org/12110042

Traschen, Jennie. Mass and Tension (momentum) Sum Rules in AdS (dS). Perimeter Institute, Nov. 27, 2012, https://pirsa.org/12110042 

@misc{ pirsa_PIRSA:12110042,
  doi = {10.48660/12110042},
  url = {https://pirsa.org/12110042},
  author = {Traschen, Jennie},
  keywords = {Quantum Gravity},
  language = {en},
  title = {Mass and Tension (momentum) Sum Rules in AdS (dS)},
  publisher = {Perimeter Institute},
  year = {2012},
  month = {nov},
  note = {PIRSA:12110042 see, \url{https://pirsa.org}}
}

Abstract

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.

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