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A singularity theorem based on spatial averages

José M. M. Senovilla
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Abstract

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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José M. M. Senovilla. 2007-05-06. A singularity theorem based on spatial averages. https://doi.org/10.1007/s12043-007-0109-2

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