
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the `violation' of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
14 pages, 3 figures, comments added on recent lqg works on boundary dynamics, refs added, version to appear in PLB
High Energy Physics - Theory, Nuclear and High Energy Physics, High Energy Physics - Theory (hep-th), Black holes, Physics, QC1-999, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, General Relativity and Quantum Cosmology, Gravitational interaction in quantum theory
High Energy Physics - Theory, Nuclear and High Energy Physics, High Energy Physics - Theory (hep-th), Black holes, Physics, QC1-999, FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, General Relativity and Quantum Cosmology, Gravitational interaction in quantum theory
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