Department of Mathematics, University of Miami, Coral Gables, Florida 33124 ; National Security Agency, Fort Meade, Maryland 20755-6000
Abstract:
A general theory of regularity for Lorentzian Busemann functions in future timelike geodesically complete spacetimes is presented. This treatment simplifies and extends the local regularity developed by Eschenburg, Galloway and Newman to prove the Lorentzian splitting theorem. Criteria for global regularity are obtained and used to improve results in the literature pertaining to a conjecture of Bartnik.