Action integrals and partition functions in quantum gravity

@article{citeulike:1320396, abstract = {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 at a certain temperature; angular momentum; and charge. We use this approach to evaluate the entropy of these metrics and find that it is always equal to one quarter the area of the event horizon in fundamental units. This agrees with previous derivations by completely different methods. In the case of a stationary system such as a star with no event horizon; the gravitational field has no entropy.}, author = {Gibbons, G. W. and Hawking, S. W. }, citeulike-article-id = {1320396}, doi = {http://dx.doi.org/10.1103/PhysRevD.15.2752}, journal = {Physical Review D}, keywords = {cosmology}, month = {May}, number = {10}, pages = {2752+}, posted-at = {2007-05-23 06:46:53}, priority = {2}, publisher = {American Physical Society}, title = {Action integrals and partition functions in quantum gravity}, url = {http://dx.doi.org/10.1103/PhysRevD.15.2752}, volume = {15}, year = {1977} }

TY - JOUR ID - citeulike:1320396 L3 - citeulike-article-id:1320396 N2 - 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 at a certain temperature; angular momentum; and charge. We use this approach to evaluate the entropy of these metrics and find that it is always equal to one quarter the area of the event horizon in fundamental units. This agrees with previous derivations by completely different methods. In the case of a stationary system such as a star with no event horizon; the gravitational field has no entropy. IS - 10 JF - Physical Review D TI - Action integrals and partition functions in quantum gravity PB - American Physical Society VL - 15 SP - 2752 KW - cosmology AU - Gibbons, GW AU - Hawking, SW PY - 1977/05/15/ UR - http://dx.doi.org/10.1103/PhysRevD.15.2752 ER -