### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 2063-2084 |

Number of pages | 22 |

Journal | Transactions of the American Mathematical Society |

Volume | 348 |

Issue number | 5 |

State | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Transactions of the American Mathematical Society*,

*348*(5), 2063-2084.

**Regularity of Lorentzian Busemann functions.** / Galloway, Gregory J; Horta, Arnaldo.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 348, no. 5, pp. 2063-2084.

}

TY - JOUR

T1 - Regularity of Lorentzian Busemann functions

AU - Galloway, Gregory J

AU - Horta, Arnaldo

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=21344431818&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21344431818

VL - 348

SP - 2063

EP - 2084

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -