Vacuum decomposition of Einstein's theory and knot topology of vacuum space-time

摘要

Viewing Einstein's theory as the gauge theory of the 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 π_3(S~3) ? π_3(S~2) of π_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.