Mathematics
Scientific paper
Dec 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986mnras.223..835b&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 223, Dec. 15, 1986, p. 835-844.
Mathematics
68
Big Bang Cosmology, Cosmology, Gravitational Collapse, Space-Time Functions, Topology, Universe, Cauchy Integral Formula, Singularity (Mathematics), Tensor Analysis
Scientific paper
It is widely believed that all expanding S3 closed universes that satisfy the standard energy conditions recollapse to a second singularity. The authors show that this is false even for Friedmann universes: they construct an ever-expanding S3 Friedmann universe in which the matter tensor satisfies the strong, weak and dominant energy conditions and the generic condition. The authors prove a general recollapse theorem for Friedmann universes: if the positive pressure criterion, dominant energy condition and matter regularity condition hold, then an S3 Friedmann universe must recollapse. The authors show that all known vacuum solutions with Cauchy surface topology S3 or S2×S1 recollapse, and they conjecture that this is a property of all vacuum solutions of Einstein's equations with such Cauchy surfaces. The authors consider a number of Kantowski-Sachs and Bianchi IX universes with various matter tensors, and formulate a new recollapse conjecture for matter-filled universes.
Barrow John D.
Galloway Gregory J.
Tipler Frank J.
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