Topology of Classical Vacuum Space-Time(VIII Asia-Pacific International Conference on Gravitation and Astrophysics (ICGA8))

Abstract

"lepresent a topological classification of vacuum space-time, Viewing Einstein'stheory as a gauge theory of Lorentzgroup and identifyingthe gravitational connection as the gauge potentialof Lorentzgroup, we construct all possible vacuum gravitationalconnections which give a vanishing curvature tensor. With this we show that, when the space-time admits a global chart, the vacuurn connection has the same topology which de$cribesthe multiple vacua of SU(2) gauge theory, This tellsthat･the vacuum space-time can be classified by the knot topology T3(S3) = T3(S2), We discussthe physical implications,in particular the space-tirne tunneling,of our result inquantum gravity.