Topologically Nontrivial Solution in Einstein-Dirac Gravity on the Hopf Bundle

Джунушалиев Владимир Джумакадырович

2018

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DOI 10.1134/s0202289318030052

Data confidence 70 medium

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Abstract

A topologically nontrivial solution in Einstein-Dirac gravity with a cosmological constant is obtained. The space-time 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. Solutions to the nongravitating Dirac equation in background Lorentzian space-time with the Hopf bundle as a spatial section are also obtained. Nongravitating solutions of the Dirac equation are characterized by two quantum half-integer numbers m , n .