A singularity theorem based on spatial averages

Details A singularity theorem based on spatial averages A singularity theorem based on spatial averages

2006-10-26

arxiv.org/abs/gr-qc/0610127v3

Pramana69:31-48,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Corrections made in the main theorem and related places. 16 pages, no figures. Invited contribution to the Pramana special iss

Scientific paper

10.1007/s12043-007-0109-2

Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables are severely geodesically incomplete to the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.

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