As discussed in the introduction, laws of black hole mechanics, discovered in the early seventies, provided a concrete challenge to candidate quantum theories of gravity: Account for the thermodynamic, black hole entropy through a detailed, statistical mechanical counting of appropriate micro-states. Indeed, this is essentially the only concrete quantitative hint we have had about the nature of quantum space-time geometry. The isolated horizon framework has been used to address this issue systematically and has led to the only available detailed calculations within a full-fledged approach to quantum gravity that encompass realistic black holes (which carry no or negligible gauge charges and may be distorted). As we will discuss in Section 8, what we know about dynamical horizons does suggest that there should be interesting generalizations of these results also to non-equilibrium situations. But so far there has been no work along these lines.

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