1994/03/28 by Arvind Borde · 2 citations
Mathematics · Physics and Astronomy · #Astrophysics #Black Holes and Theoretical Physics #Classical mechanics #Closed timelike curve #Convergence (economics) #Cosmology and Gravitation Theories #Economics #Gravitational singularity #Inflation (cosmology) #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Relativity and Gravitational Theory #Singularity #Spacetime #Theoretical physics #Universe #gr-qc
paper · pdf · doi:10.1103/physrevd.50.3692
published as Phys.Rev. D50 (1994) 3692-3702 · 27 pages, Plain TeX (figures are embedded in the file itself and they will emerge if it is processed according to the instructions at the top of the file)
arxiv created 1994/03/28 · openalex publication_date 1994/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a) previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b) the timelike convergence condition is known to be violated in inflationary spaceitmes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may not be extended to include many closed universes. Also, as a fringe benefit, the time reverse of the theorem may be applied to gravitational collapse.