Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon
May, 2011Citations per year
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 . (When the generalized entropy is not invariant under local Lorentz boosts.) It is shown that a certain second null derivative of the entropy, , 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 . 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
References(22)
Figures(2)