The first law for slowly evolving horizons.

@article{Booth2004TheFL,
  title={The first law for slowly evolving horizons.},
  author={Ivan S. N. Booth and Stephen Fairhurst},
  journal={Physical review letters},
  year={2004},
  volume={92 1},
  pages={011102}
}
We study the mechanics of Hayward's trapping horizons, taking isolated horizons as equilibrium states. Zeroth and second laws of dynamic horizon mechanics come from the isolated and trapping horizon formalisms, respectively. We derive a dynamical first law by introducing a new perturbative formulation for dynamic horizons in which "slowly evolving" trapping horizons may be viewed as perturbatively nonisolated. 
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