Quantum properties of non-Dirichlet boundary conditions in gravity

Journal Article · Fri Feb 13 00:00:00 EST 2026 · Physical Review D

DOI:https://doi.org/10.1103/nwpg-5mld· OSTI ID:3025439

Draper, Patrick ^[1]; Karydas, Manthos ^[2]; Zhang, Hao ^[1]

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1. University of Illinois
2. Lawrence Berkeley National Laboratory

The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric; microcanonical conditions, which refers to fixing some components of the Brown-York boundary stress tensor; and conformal conditions, in which the conformal structure of the induced metric and the trace of the extrinsic curvature are fixed. Boundaries also present interesting problems of consistency. The Dirichlet problem is known, under various (and generally different) conditions, to be inconsistent with perturbative quantization of graviton fluctuations, to exhibit thermodynamic instability, or to require infinite fine-tuning in the presence of matter fluctuations. We extend some of these results to other boundary conditions. We find that similarly to the Dirichlet problem, the graviton fluctuation operator is not elliptic with microcanonical boundaries, and the nonelliptic modes correspond to “boundary-moving diffeomorphisms.” However, we argue that microcanonical factorization of path integrals—essentially, the insertion of microcanonical constraints on two-sided surfaces in the bulk—is not affected by the same issues of ellipticity. We also show that for a variety of matter field boundary conditions, matter fluctuations renormalize the gravitational bulk and boundary terms differently, so that the classical microcanonical or conformal variational problems are not preserved unless an infinite fine-tuning is performed.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: High Energy Physics; Office of Science; U.S. Department of Energy
• Grant/Contract Number: AC02-05CH11231; SC0015655
• OSTI ID: 3025439
• Journal Information: Physical Review D, Journal Name: Physical Review D Journal Issue: 4 Vol. 113; ISSN 2470-0010; ISSN 2470-0029
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English