TY - GEN
T1 - Singularities and quantum gravity
AU - Bojowald, Martin
PY - 2007
Y1 - 2007
N2 - Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria for non-singular behavior are often unclear or controversial. Often, only special types of singularities such as the curvature singularities found in isotropic cosmological models are discussed and it is far from clear what this implies for the very general singularities that arise according to the singularity theorems of general relativity. In these lectures we present an overview of the current status of singularities in classical and quantum gravity, starting with a review and interpretation of the classical singularity theorems. This suggests possible routes for quantum gravity to evade the devastating conclusion of the theorems by different means, including modified dynamics or modified geometrical structures underlying quantum gravity. The latter is most clearly present in canonical quantizations which are discussed in more detail. Finally, the results are used to propose a general scheme of singularity removal, quantum hyperbolicity, to show cases where it is realized and to derive intuitive semiclassical pictures of cosmological bounces.
AB - Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria for non-singular behavior are often unclear or controversial. Often, only special types of singularities such as the curvature singularities found in isotropic cosmological models are discussed and it is far from clear what this implies for the very general singularities that arise according to the singularity theorems of general relativity. In these lectures we present an overview of the current status of singularities in classical and quantum gravity, starting with a review and interpretation of the classical singularity theorems. This suggests possible routes for quantum gravity to evade the devastating conclusion of the theorems by different means, including modified dynamics or modified geometrical structures underlying quantum gravity. The latter is most clearly present in canonical quantizations which are discussed in more detail. Finally, the results are used to propose a general scheme of singularity removal, quantum hyperbolicity, to show cases where it is realized and to derive intuitive semiclassical pictures of cosmological bounces.
UR - http://www.scopus.com/inward/record.url?scp=34548848539&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34548848539&partnerID=8YFLogxK
U2 - 10.1063/1.2752483
DO - 10.1063/1.2752483
M3 - Conference contribution
AN - SCOPUS:34548848539
SN - 0735404186
SN - 9780735404182
T3 - AIP Conference Proceedings
SP - 294
EP - 333
BT - COSMOLOGY AND GRAVITATION
T2 - COSMOLOGY AND GRAVITATION: XIIth Brazilian School of Cosmololy and Gravitation
Y2 - 10 September 2006 through 23 September 2006
ER -