Asymptotic Analysis of Field Commutators for Einstein-Rosen Gravitational Waves

Details Asymptotic Analysis of Field Commutators for Einstein-Rosen Gravitational Waves Asymptotic Analysis of Field Commutators for Einstein-Rosen Gravitational Waves

2004-05-14

arxiv.org/abs/gr-qc/0405075v1

J.Math.Phys.45:3498-3532,2004

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages in DIN A4 format, 9 figures. Accepted in Journal of Mathematical Physics

Scientific paper

10.1063/1.1769612

We give a detailed study of the asymptotic behavior of field commutators for linearly polarized, cylindrically symmetric gravitational waves in different physically relevant regimes. We also discuss the necessary mathematical tools to carry out our analysis. Field commutators are used here to analyze microcausality, in particular the smearing of light cones owing to quantum effects. We discuss in detail several issues related to the semiclassical limit of quantum gravity, in the simplified setting of the cylindrical symmetry reduction considered here. We show, for example, that the small G behavior is not uniform in the sense that its functional form depends on the causal relationship between spacetime points. We consider several physical issues relevant for this type of models such as the emergence of large gravitational effects.

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