Topologically nontrivial solution in Einstein-Dirac gravity on the Hopf bundle

Vladimir Dzhunushaliev

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arXiv · 1612.07149

Topologically nontrivial solution in Einstein-Dirac gravity on the Hopf bundle

Vladimir Dzhunushaliev

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Abstract

The topologically nontrivial solution in Einstein-Dirac gravity with cosmological constant is obtained. The spacetime has the Hopf bundle as a spatial section. It is shown that the Hopf invariant is related to the spinor current density. Two Dirac spinors are used for obtaining a diagonal energy-momentum tensor. The solutions for the nongravitating Dirac equation on the background of Lorentzian spacetime with the Hopf bundle as a spatial section are also obtained. Nongravitating solutions of the Dirac equation are defined by two quantum half-integer numbers $m, n$.

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Vladimir Dzhunushaliev. 2016-12-17. Topologically nontrivial solution in Einstein-Dirac gravity on the Hopf bundle. https://arxiv.org/abs/1612.07149

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