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Mathematical and Theoretical Physics Seminar: Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity

Event Type
Seminar/Symposium
Sponsor
Physics Department
Location
Loomis Room 464
Date
Aug 29, 2024   1:00 pm  
Speaker
Xiaoyi Liu, University of California, Santa Barbara
Contact
Ljubica Milutinovic
E-Mail
ljubicam@illinois.edu
Phone
217-300-6393
Views
51
Originating Calendar
Physics - Mathematical and Theoretical Physics Seminar

We consider four-dimensional Euclidean gravity in a finite cavity.  We point out that there exists a one-parameter family of boundary conditions, parameterized by a real constant, where a suitably Weyl-rescaled boundary metric is fixed, and all give a well-posed elliptic system, as opposed to the Dirichlet boundary condition. Focussing on static Euclidean solutions, we derive a thermodynamic first law. Restricting to a spherical spatial boundary, the infillings are flat space or the Schwarzschild solution, and have similar thermodynamics to the Dirichlet case. We study the stability behavior of several geometries under these boundary conditions in both Euclidean and Lorentzian signatures and find two puzzles.

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