The imaginary part of the gravitational action and black hole entropy

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I present a candidate for a new derivation of black hole
entropy. The key observation is that the action of General Relativity in
bounded regions has an imaginary part, arising from the boundary term. The
formula for this imaginary part is closely related to the Bekenstein-Hawking
entropy formula, and coincides with it for certain classes of regions. This
remains true in the presence of matter, and generalizes appropriately to
Lovelock gravity. The imaginary part of the action is a versatile notion,
requiring neither stationarity nor any knowledge about asymptotic infinity.
Thus, it may provide a handle on quantum gravity in finite and dynamical
regions. I derive the above results, make connections with standard approaches
to black hole entropy, and speculate on the meaning of it all. Implications for
loop quantum gravity are also discussed.