Black-hole models in loop quantum gravity

TL;DR

This paper reviews loop quantum gravity black-hole models, highlighting issues with covariance in previous models and emphasizing the need for a generalized, covariant space-time structure derived from canonical gravity constraints.

Contribution

It critically analyzes existing loop quantum gravity black-hole models, demonstrating their violations of covariance, and discusses the necessity of a generalized covariant space-time framework.

Findings

Most previous models violate general covariance.

A new covariant space-time structure is necessary.

Implications for black-hole physics are discussed.

Abstract

Dynamical black-hole scenarios have been developed in loop quantum gravity in various ways, combining results from mini and midisuperspace models. In the past, the underlying geometry of space-time has often been expressed in terms of line elements with metric components that differ from the classical solutions of general relativity, motivated by modified equations of motion and constraints. However, recent results have shown by explicit calculations that most of these constructions violate general covariance and slicing independence. The proposed line elements and black-hole models are therefore ruled out. The only known possibility to escape this sentence is to derive not only modified metric components but also a new space-time structure which is covariant in a generalized sense. Formally, such a derivation is made available by an analysis of the constraints of canonical gravity, which generate deformations of hypersurfaces in space-time, or generalized versions if the constraints are consistently modified. Implications for black holes are described here. [Abbreviated abstract]