Spin-spin interaction in general relativity and induced geometries with nontrivial topology

V.G. Krechet and D.V. Sadovnikov1


We consider the dynamics of a self-gravitating spinor field and a self-gravitating rotating perfect fluid. It is shown that both these matter distributions can induce a vortex field described by the curl 4-vector of a tetrad: wi = [ 1/2]epsiklme(a)ke(a)l;m, where e(a)k are components of the tetrad. The energy-momentum tensor Tik(w) of this field has been found and shown to violate the strong and weak energy conditions which leads to possible formation of geometries with nontrivial topology like wormholes. The corresponding exact solutions to the equations of general relativity have been found. It is also shown that other vortex fields, e.g., the magnetic field, can also possess such properties.


  1. V. G. Krechet, Izv. Vuzov, Fizika, No. 3, 3-6 (2005).
  2. V. G. Krechet and D. V. Sadovnikov, Grav. & Cosmol. 13 269 (2007).
  3. V. G. Krechet, M. V. Levkoeva, E. Orlova, and D. V. Sadovnikov, Abstracts of the 12th Russian Gravitational Conference, Kazan, 2005, p. 149-150.
  4. V. G. Krechet and D. V. Sadovnikov, in: Reports of the Scientific and Practical Conference "Integration of Education and Science" (MGPTU, Prometei publishers, Moscow, 2009), pp. 63-69.
  5. H. Ellis, J. Math. Phys. 14, 104 (1973).
  6. K. A. Bronnikov, Acta Phys. Pol. B 4, 251 (1973).
  7. K. A. Bronnikov and J. P. S. Lemos, Phys. Rev. D 79, 104019 (2009); ArXiv: 0902.2360.
  8. K. A. Bronnikov, Izv. Vuzov, Fizika, No. 6, 37 (1979); in: Problems of Gravitation Theory and Particle Theory (Atomizdat, Moscow, 1979, 10th issue, in Russian), pp. 37-50.
  9. Yu. S. Vladimirov, Reference Frames in Gravitation Theory (Energoizdat, Moscow, 1982, in Russian).
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