A singularity theorem based on spatial averages |
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Authors: | J. M. M. Senovilla |
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Affiliation: | (1) Física Teórica, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain |
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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 Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in 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. In memory of Amal Kumar Raychaudhuri (1924–2005). |
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Keywords: | Raychaudhuri equation singularity-free cosmologies singularity theorems |
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