Xiaoyi Liu - Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity

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Mathematical and Theoretical Physics Seminar 8/29/2024

Speaker: Xiaoyi Liu, University of California, Santa Barbara

Title: Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity

Abstract: 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. Focusing 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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Xiaoyi Liu - Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity

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