2007

Abstract:

The problem of N-body motion for non-relativistic self-gravitating systems has a long standing history. Recent work on this subject has shown that this problem can be extended to a fully generally relativistic scenario. Exact solutions for the Hamiltonian for the 2-body case are given in terms of the Lambert-W function. When extended to situations that include any or all of cosmological expansion, electromagnetic charge, or more than 2 bodies, solutions can be expressed in terms of natural generalizations of the Lambert W-function. I shall provide an overview of these results that describe the foundations of these models, the exact solutions in terms of the W-function and its generalizations, and numerical work on chaotic phenomena in the 3-body case.