Smoothing and extending cosmic time functions

Details Smoothing and extending cosmic time functions Smoothing and extending cosmic time functions

Oct 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..815s&link_type=abstract

General Relativity and Gravitation, vol. 8, Oct. 1977, p. 815-831.

Astronomy and Astrophysics

Astrophysics

14

Astrophysics, Relativity, Smoothing, Space-Time Functions, Applications Of Mathematics, Hyperbolic Functions, Hyperspaces

Scientific paper

Basic principles of smoothing a time function and of construction extensions of time functions on a stably causal spacetime are noted. The 'zoology' of spacelike hypersurfaces is discussed, and a theorem of relevance to covering by slices and causality is given together with several lemmas and proofs. Theorems, proofs, and lemmas are also presented which relate to a formalism for making time functions uniform and regular. A three-step procedure is outlined for extending time functions onto the whole of a stably causal spacetime.

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