Action Integrals and Partition Functions in Quantum Gravity

@article{Gibbons1977ActionIA,
  title={Action Integrals and Partition Functions in Quantum Gravity},
  author={G. W. Gibbons and Stephen William Hawking},
  journal={Physical Review D},
  year={1977},
  volume={15},
  pages={2752-2756}
}
One can evaluate the action for a gravitational field on a section of the complexified spacetime which avoids the singularities. In this manner we obtain finite, purely imaginary values for the actions of the Kerr-Newman solutions and de Sitter space. One interpretation of these values is that they give the probabilities for finding such metrics in the vacuum state. Another interpretation is that they give the contribution of that metric to the partition function for a grand canonical ensemble… 
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