An Alternate Path Integral for Quantum Gravity

Abstract

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.

29 pages, v3: references and a concluding speculative comment added

References in corpus (10)

• Generalized gravitational entropy
• Aspects of AdS/BCFT
• Setting the boundary free in AdS/CFT
• A Boundary Term for the Gravitational Action with Null Boundaries
• Finite action principle for Chern-Simons AdS gravity
• Conformal gravity holography in four dimensions
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• Consistent boundary conditions for supergravity
• Black Hole Vacua and Rotation
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• A Neumann Boundary Term for Gravity
• Lessons for quantum cosmology from anti-de Sitter black holes
• A Dynamical Boundary for Anti-de Sitter Space
• Robin Gravity
• Scalar field condensation behaviors around reflecting shells in Anti-de Sitter spacetimes
• Boundary dynamics in gravitational theories
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• Foliation-based quantization and black hole information
• Chiral Higher Spin Gravity
• Foliation-based approach to quantum gravity and applications to astrophysics
• Bulk Locality and Asymptotic Causal Diamonds
• Quantum gravitational effects on boundary
• HKLL for the Non-Normalizable Mode
• Motion of Particles in Solar and Galactic Systems by Using Neumann Boundary Condition
• Quantization of gravity and finite temperature effects
• Nakanishi-Kugo-Ojima quantization of general relativity in Heisenberg picture
• A Hairy Box in Three Dimensions
• On the classification of consistent boundary conditions for $f(R)$-Gravity
• Local Stability of Galactic Discs in Modified Dynamics
• The fate of boundary terms in dimensional reductions