Action Integrals and Partition Functions in Quantum Gravity

  title={Action Integrals and Partition Functions in Quantum Gravity},
  author={G. W. Gibbons and Stephen William Hawking},
  journal={Physical Review D},
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… 
Thermodynamics, Euclidean Gravity and Kaluza-Klein Reduction
The aim of this paper is to find a correspondence between the one-loop effective action WE defined by means of a path integral in Euclidean gravity and the free energy F obtained by summation over
Supersymmetric indices factorize
The extent to which quantum mechanical features of black holes can be understood from the Euclidean gravity path integral has recently received significant attention. In this paper, we examine this
The Gravitational Hamiltonian, action, entropy and surface terms
We give a derivation of the gravitational Hamiltonian starting from the Einstein - Hilbert action, keeping track of all surface terms. This derivation can be applied to any spacetime that
Chiral vacuum fluctuations in quantum gravity
In this paper we investigate cosmological tensor modes in terms of the Ashtekar variables of loop quantum gravity, for complex values of the Immirzi parameter. While, on-shell, the classical
Effective Lagrangian for quantum black holes
We discuss the most general effective Lagrangian obtained from the assumption that the degrees of freedom to be quantized, in a black hole, are on the horizon. The effective La- grangian depends only
Zero-point quantum fluctuations in cosmology
We re-examine the classic problem of the renormalization of zero-point quantum fluctuations in a Friedmann-Robertson-Walker background. We discuss a number of issues that arise when regularizing the
The two-sphere partition function in two-dimensional quantum gravity
Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem
An alternative path integral for quantum gravity
A bstractWe define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean
Finite action principle for chern-simons ads gravity
A finite action principle for Chern-Simons AdS gravity is presented. The construction is carried out in detail first in five dimensions, where the bulk action is given by a particular combination of
In these lectures I am going to describe an approach to Quantum Gravity using path integrals in the Euclidean regime i.e. over positive definite metrics. (Strictly speaking, Riemannian would be more