Regularity of Lorentzian Busemann Functions

Galloway, Gregory; Horta, Arnaldo

doi:10.1090/S0002-9947-96-01587-5

Regularity of Lorentzian Busemann Functions
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by Gregory J. Galloway and Arnaldo Horta

Trans. Amer. Math. Soc. 348 (1996), 2063-2084

DOI: https://doi.org/10.1090/S0002-9947-96-01587-5

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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.

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