Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon

May, 2011
14 pages
Published in:
  • Phys.Rev.D 85 (2012) 024015
e-Print:

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Abstract: (arXiv)
The anomalous conformal transformation law of the generalized entropy is found for dilaton gravity coupled to a 1+1 conformal matter sector with central charges c=c~c = \tilde{c}. (When cc~c \ne \tilde{c} the generalized entropy is not invariant under local Lorentz boosts.) It is shown that a certain second null derivative of the entropy, Sgen"+(6/c)(Sout)2S_\text{gen}" + (6/c)(S_\text{out}')^2, is primary, and therefore retains its sign under a general conformal transformation. Consequently all conformal vacua have increasing entropy on causal horizons. Alternative definitions of the horizon, including apparent or dynamical horizons, can have decreasing entropy in any dimension D2D \ge 2. This indicates that the generalized second law should be defined using the causal horizon.
Note:
  • 19 pages, 2 figures, v2 significant additions clarifying sections 3, 5, and 6, v3 fixed typo in Eq. (35)
  • 04.70.Dy
  • 04.62.+v
  • 04.60.Kz
  • transformation: conformal
  • gravitation: dilaton
  • dimension: 2
  • entropy
  • vacuum state
  • central charge
  • causality