The Kerr Spinning Particle and Associated Wave-Pilot Construction

Alexander Burinskii
Gravity Research Group
NSI Russian Academy of Sciences
B.Tulskaya 52 , 115191
Moscow, RUSSIA
email: bur@ibrae.ac.ru

The Kerr rotating black hole solution displays some remarkable relations to the spinning particles [1-6]. In particular, the gyromagnetic ratio of the charged solution is the same as that of the Dirac electron [1]. For parameters of elementary particles the black-hole horizons disappear and the source of the Kerr spinning particle represents a closed singular ring of the Compton radius. This ring can be used as a gravitational waveguide for a circular motion of a light-like particle (photon), forming a microgeon with spin [2]. The corresponding field model has to be described by the solutions of the Einstein-Maxwell field equations containing the circular traveling e.m. waves. It was suggested [3] that this singular ring plays the role of a closed string of the dual models of elementary particles. However, up to the recent time, it was known only on the level of evidences, sometime rather convincing. In particular, A.Sen has obtained a generalization of the Kerr solution to low energy string theory [6]. It was shown [7] that the fields near the Kerr singular ring in this solution are very similar to the fields around fundamental heterotic string. In the present talk we consider the real and complex structures of the Kerr geometry and show that the Kerr singular ring satisfies to the string equations with an orientifold structure. We show also that the classical model of the Kerr particle has some quantum exhibitions. For example, oscillations of the Kerr string does not lead to the loss of energy via radiation being compensated by the in-going advanced fields of the zero-point fluctuations. Finally, basing on the recent progress in the obtaining of the nonstationary Kerr solutions [8], we show that the e.m. excitations of the Kerr singular ring lead unavoidably to the appearance of the second (axial) singular line. The propagating along this axial string traveling waves are modulated by the de Broglie periodicity. This singularity is topologically coupled with the Kerr ring threading it and extends to infinity [9]. Because of the topological coupling, the position and propagation of the Kerr ring is controlled by the position of the axial singularity, reproducing the old de Broglie idea. Like the monopole string, the axial string is fixed by the gauge fields. However, the gauge is not free in the topologically non-trivial situations caused by the presence of external objects. We discuss also briefly the relation of this model to the modern superstring theory, D-branes and compactification.

References

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