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The physical process version of the first law for black holes states that the passage of energy and angular momentum through the horizon results in a change in area $\frac{\kappa}{8 \pi} \Delta A = \Delta E - \Omega \Delta J$, so long as this passage is quasi-stationary.
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A. Bergman, J. Distler, and U. Varadarajan, “1+1 dimensional critical string theory and holography,” [arXiv:hep-th/0312115]
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