Quantum "violation" of Dirichlet boundary condition

Abstract

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

References in corpus (5)

• Gravitational action with null boundaries
• A "general boundary" formulation for quantum mechanics and quantum gravity
• Non-equilibrium Condensation Process in a Holographic Superconductor
• The loop gravity string
• A Dynamical Boundary for Anti-de Sitter Space

Cited by in corpus (10)

• Quantum-induced trans-Planckian energy near horizon
• Boundary dynamics in gravitational theories
• Quantum-corrected geometry of horizon vicinity
• Black hole evolution in quantum-gravitational framework
• Foliation-based quantization and black hole information
• Foliation-based approach to quantum gravity and applications to astrophysics
• Quantum gravitational effects on boundary
• Revisit of renormalization of Einstein-Maxwell theory at one-loop
• Quantum-gravitational trans-Planckian energy of a time-dependent black hole
• Channel induced dynamics of quantum information in mixed state free QFTs