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.
|Original language||English (US)|
|Number of pages||22|
|Journal||Transactions of the American Mathematical Society|
|State||Published - Dec 1 1996|
ASJC Scopus subject areas
- Applied Mathematics