Quantum "violation" of Dirichlet boundary condition

TL;DR

This paper explores how quantum effects in gravity can lead to violations of classical Dirichlet boundary conditions, revealing a tension between boundary conditions and quantum information storage in black holes.

Contribution

It demonstrates that quantum corrections cause black hole solutions to deviate from classical Dirichlet boundary conditions, highlighting a novel quantum-gravity boundary phenomenon.

Findings

Quantum-corrected black holes do not strictly obey classical Dirichlet conditions.

A mechanism of boundary information storage explains the apparent violation.

The work suggests a fundamental tension between boundary conditions and quantum gravity effects.

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.