Gravitational fields and harmonic gauge in brane model of Universe
We suppose that our Universe is closed manifold in real embedding higher dimensional space. This model well describes expanding character of Universe where each point becomes more far from any other point with time. We have derived Klein-Gordon equation using the symmetry of Universe expansion. Comparing it with squared Dirac-Fock-Ivanenko equation we have derived expression for gravitationally induced chiral current. Starting from the expression for gravitationally induced chiral current obtained on the basis of brane symmetry we have shown that being placed into the Einstein's gravitational field, chiral current yields inertial gravitational field. This inertial gravitational field transforms into the vortex gravitational field and then back to the inertial gravitational field thus ensuring the propagation of such kind of gravitational excitation as constitutional part of gravitational wave. In the case of weak gravitation, these symmetry considerations and our consequent equations lead directly to harmonic gauge conditions that are necessary for supplementing Einstein equations.