# Compact four–dimensional euclidean space embedded in the universe

@article{Kurihara2016CompactFE, title={Compact four–dimensional euclidean space embedded in the universe}, author={Yoshimasa Kurihara}, journal={Physics \& Astronomy International Journal}, year={2016} }

A compact four-dimensional manifold whose metric tensor has a positive determinant (named the "Euclid ball") is considered. The Euclid ball can be immersed in the Minkovskian space (which has the negative determinant) and can exist stably through the history of the universe. Since the Euclid ball has the same solution as the Schwarzschild black hole on its three-dimensional surface, an asymptotic observer can not distinguish them. If large fraction of whole energy of the pre-universe was…

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