Effective line elements and black-hole models in canonical (loop) quantum gravity

TL;DR

This paper develops a framework for deriving effective space-time structures in canonical quantum gravity, revealing signature change and providing a new perspective on black-hole interiors within loop quantum gravity.

Contribution

It introduces a method to derive unambiguous effective line elements from anomaly-free constraints, highlighting signature change and applying it to black-hole models in loop quantum gravity.

Findings

Signature change is an inevitable consequence of non-classical gauge transformations.

A self-consistent space-time structure for black holes is established.

The framework clarifies the relationship between quantum constraints and space-time geometry.

Abstract

Canonical quantization is often used to suggest new effects in quantum gravity, in the dynamics as well as the structure of space-time. Usually, possible phenomena are first seen in a modified version of the classical dynamics, for instance in an effective Friedmann equation, but there should also be implications for a modified space-time structure. Quantum space-time effects, however, are often ignored in this setting because they are not obvious: they require a careful analysis of gauge transformations and the anomaly problem. It is shown here how modified space-time structures and effective line elements can be derived unambiguously, provided an off-shell anomaly-free system of modified constraints exists. The resulting effective line elements reveal signature change as an inescapable consequence of non-classical gauge transformations in the presence of holonomy modifications. The general framework is then specialized to black-hole models in loop quantum gravity. In contrast to previous studies, a self-consistent space-time structure is taken into account, leading to a new picture of black-hole interiors.