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 quantumcorrected 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. arXiv:1609.06251v3 [hep-th] 9 Dec 2016 1 It was stated that inclusion of all of the possible boundary conditions is necessary for the complete Hilbert space. This seems to be in line with the AdS/CFT, and the present work shares the spirit.

Quantum-induced trans-Planckian energy near horizon

“…Since this could be achieved without adding the Gibbons-Hawking term, the boundary condition was not restricted to the Dirichlet. Another not-so-obvious implication is that one must check whether or not the classical-level boundary conditions are honored by the quantum corrections [28]. (In section 3 we will push further along this direction.)…”

“…The influence of quantum effects on the geometry is quite natural [19] [21]. The way the boundary conditions figure into the mutual relations has just been recognized [28,29]. One of the focuses of the present work is the manner in which the quantum effects and boundary conditions feed the time-dependence of a solution.…”

“…A meaningful observation on the boundary conditions as a crucial component of the Hilbert space has recently been put forth in loop quantum gravity works [26] and [27]. Although the widely-used Dirichlet boundary conditions have been successful in non-gravitational areas, narrowing down to the configurations with these boundary conditions in a gravity theory results in wipe-out of much of the information as demonstrated in the recent works [19,22,28,29]. The surprising fact that the Dirichlet boundary condition is at odds with the information of the system seems quite sophisticated, and must be due to the fact that the physical states of a gravitational system happen to have their support at the boundary hypersurface, the holographic screen, which in turn has its origin in the large amount of the gauge symmetry of a gravitational system [30].…”

Quantum-Gravitational Trans-Planckian Energy of a Time-Dependent Black Hole

“…The classical part of the quantum-level solution is required to settle down to a Kerr geometry. A novel feature observed in [15,16] is shared: the quantum effects remove the time-dependence of the classical part, which is crucial for the subsequent energy analysis. In section 4, we analyze the energy observed near horizon by an infalling observer and are led to a trans-Planckian energy.…”

Foliation-Based Approach to Quantum Gravity and Applications to Astrophysics

“…There are several prominent indications of the relevance of the non-Dirichlet boundary conditions. For instance, it has recently been shown that quantum corrections are at odds with the Dirichlet boundary condition [66] [67]. Another indication comes from the recent development along the line of BMS symmetry [68] [69] where renewed attention has been given to large gauge transformations (LGTs).…”