Spherically Symmetric Solution for Torsion and the Dirac equation in 5D spacetime

Details Spherically Symmetric Solution for Torsion and the Dirac equation in 5D spacetime Spherically Symmetric Solution for Torsion and the Dirac equation in 5D spacetime

1998-06-09

arxiv.org/abs/gr-qc/9806046v2

Int.J.Mod.Phys.D7:909-915,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, REVTEX, essential changing of text

Scientific paper

10.1142/S0218271898000590

Torsion in a 5D spacetime is considered. In this case gravitation is defined by the 5D metric and the torsion. It is conjectured that torsion is connected with a spinor field. In this case Dirac's equation becomes the nonlinear Heisenberg equation. It is shown that this equation has a discrete spectrum of solutions with each solution being regular on the whole space and having finite energy. Every solution is concentrated on the Planck region and hence we can say that torsion should play an important role in quantum gravity in the formation of bubbles of spacetime foam. On the basis of the algebraic relation between torsion and the classical spinor field in Einstein-Cartan gravity the geometrical interpretation of the spinor field is considered as ``the square root'' of torsion.

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