A nonsingular, anisotropic universe in a black hole with torsion and particle production

Abstract

We consider a universe formed in a black hole in general relativity with spin and torsion. The interior of a Schwarzschild black hole can be represented by the Kantowski$-$Sachs metric that describes a closed anisotropic universe. We use this metric to derive the Einstein$-$Cartan field equations with a relativistic spin fluid as a source. We show that torsion may prevent a singularity and replace it with a nonsingular bounce if particle production dominates over shear. Particle production after the last bounce can generate a finite period of inflation, during which the universe expands and isotropizes to the current state. This scenario is only approximate: the Kantowski$-$Sachs metric is never reached and should be replaced with a more general metric that tends to that of a 3-sphere.

9 pages; published version

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• A simple direct empirical observation of systematic bias of the redshift as a distance indicator