Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 10, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP10(2016)043
Keywords
AdS-CFT Correspondence; Black Holes; Classical Theories of Gravity
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We 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 quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This Neumann ensemble perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
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