Area, Entanglement Entropy and Supertranslations at Null Infinity

Mar 24, 2016
10 pages
Published in:
  • Class.Quant.Grav. 34 (2017) 16, 165007
  • Published: Jul 26, 2017
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Abstract: (IOP)
The area of a cross-sectional cut Σ\Sigma of future null infinity (I+ \newcommand{\ip}{{{\mathcal I}}^+} \ip ) is infinite. We define a finite, renormalized area by subtracting the area of the same cut in any one of the infinite number of BMS-degenerate classical vacua. The renormalized area acquires an anomalous dependence on the choice of vacuum. We relate it to the modular energy, including a soft graviton contribution, of the region of I+ \newcommand{\ip}{{{\mathcal I}}^+} \ip to the future of Σ\Sigma . Under supertranslations, the renormalized area shifts by the supertranslation charge of Σ\Sigma . In quantum gravity, we conjecture a bound relating the renormalized area to the entanglement entropy across Σ\Sigma of the outgoing quantum state on I+ \newcommand{\ip}{{{\mathcal I}}^+} \ip .
Note:
  • 14 pages
  • entropy: entanglement
  • quantum gravity
  • vacuum state
  • gravitation
  • graviton
  • modular