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Testing the generalized second law in 1+1 dimensional conformal vacua: An argument for the causal horizon

Aron C. Wall*

  • Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20740-4111, USA

  • *aronwall@umd.edu
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Phys. Rev. D 85, 024015 – Published 12 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.024015

Abstract

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˜. (When c≠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′)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 D≥2. This indicates that the generalized second law should be defined using the causal horizon.

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Phys. Rev. D 85, 024015– Published 12 January, 2012
  • Received 24 May 2011
Article part of CHORUS

© 2012 American Physical Society

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