Loop Quantum Gravity and Asymptotically Flat Spaces

Details Loop Quantum Gravity and Asymptotically Flat Spaces Loop Quantum Gravity and Asymptotically Flat Spaces

2000-08-15

arxiv.org/abs/gr-qc/0008038v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, based on talk presented at the MG IX meeting in Rome, July 2000

Scientific paper

After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector based on the GNS construction. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. States in these Hilbert spaces can be interpreted as describing fluctuations around fiducial fixed backgrounds. When the backgrounds are chosen to approximate classical asymptotically flat 3-geometries this gives a natural framework in which to discuss physical applications of loop quantum gravity, especially its semi-classical limit. We present three general proposals for the construction of suitable backgrounds, including one approach that can lead to quantum gravity on anti-DeSitter space as described by the Chern-Simons state.

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