A TOPOLOGICAL EXTENSION OF GENERAL-RELATIVITY

A see of algebraic equations for the topological properties of space-t ime is derived, and used to extend general relativity into the Planck domain. A unique basis set of three-dimensional prime manifolds is con structed which consists of S-3, S-1 x S-2, and T-3. The action of a lo op algebra on these prime manifolds yields topological invariants whic h constrain the dynamics of the four-dimensional space-time manifold. An extended formulation of Mach's principle and Einstein's equivalence of inertial and gravitational mass is proposed which leads to the cor rect classical limit of the theory. It is found that the vacuum posses ses four topological degrees of freedom corresponding to a lattice of three-tori. This structure for the quantum foam naturally leads to gau ge groups O(n) and SU(n) for the fields, a boundary condition for the universe, and an initial state characterized by local thermal equilibr ium. The current observational estimate of the cosmological constant i s reproduced without fine-tuning and found to be proportional to the n umber of macroscopic black holes. The black hole entropy follows immed iately from the theory and the quantum corrections to its Schwarzschil d horizon are computed. (C) 1997 Published by Elsevier Science B.V.