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- The imaginary part of the gravitational action and black hole entropy

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13040106

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.

©2012 Perimeter Institute for Theoretical Physics