Knot Topology of Vacuum Space-Time and Vacuum Decomposition of Einstein's Theory

Details Knot Topology of Vacuum Space-Time and Vacuum Decomposition of Einstein's Theory Knot Topology of Vacuum Space-Time and Vacuum Decomposition of Einstein's Theory

2011-10-28

arxiv.org/abs/1110.6238v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

Viewing Einstein's theory as the gauge theory of Lorentz group, we construct the most general vacuum connections which have vanishing curvature tensor and show that the vacuum space-time can be classified by the knot topology $\pi_3(S^3)\simeq \pi_3(S^2)$ of $\pi_3(SO(3,1))$. With this we obtain the gauge independent vacuum decomposition of Einstein's theory to the vacuum and gauge covariant physical parts. We discuss the physical implications of our result in quantum gravity.

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