Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon
نویسنده
چکیده
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 = c̃. (When c 6= c̃ the generalized entropy is not invariant under local Lorentz boosts.) It is shown that a certain second null derivative of the entropy, S′′ gen + (6/c)(S ′ out) , 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 D ≥ 2. This indicates that the generalized second law should be defined using the causal horizon. PACS numbers: 04.70.Dy, 04.62.+v, 04.60.Kz
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