Stability of the lepton bag model based on the Kerr–Newman solution

Abstract

We show that the considered in previous paper [1] lepton bag model, generating the external gravitational and electromagnetic fields of the Kerr-Newman (KN) solution is supersymmetric and represents a BPSsaturated soliton, interpolating between internal vacuum state and external KN solution. We obtain Bogomolnyi equations for this phase transition, and show that Bogomolnyi bound determines all important features of this bag model, including its stable shape. In particular, for stationary KN solution the BPS-bound provides stability of the ellipsoidal form of the bag and formation of the ring-string structure at its border, while for the periodic electromagnetic excitations of the KN solution, the BPS-bound controls deformation of the surface of the bag, reproducing the known flexibility of bag models. This paper is extension of the work [1], in which we considered the gravitating lepton bag model based on the Kerr-Newman (KN) black hole solution.It has been discussed long ago that black holes may be connected with elementary particles. However, the spin/mass ratio of elementary particles is extreme large, and the corresponding black hole loses the horizons, turning into an ultra-extreme (over-charged and over-rotating) KN solution with a naked singular ring, which forms a topological defect of space-time. As usual, emergence of singularity is a hint for generalization of the theory, and the Kerr singular ring created the problem of source of the KN solution. This problem proved to be very complicated, and this year we can mark the 50th anniversary of its discussions. Earlier attempts to build a source of the KN solution where discussed by Israel in [2], and Israel referred to the paper by Newman and Janis 1965 [3], wherein nontriviality of this problem was at first indicated. Carter obtained in [4] that the KN solution has gyromagnetic ratio g = 2, corresponding to that of the Dirac electron, and starting from this fact, Israel suggested in [2] a classical model of the electron based on a rotating disklike source of the KN solution, enclosed by the Kerr singular ring.The consistent regular model of the KN source was suggested by López, who built the KN source as a rotating vacuum bubble, covering the Kerr singular ring. In the same time, many properties of the KN source indicated its close relationships with string models [5,6,7,8], and resolution of this duality was coming from the disklike soliton model [9], in which the vacuum internal state of the López bubble-source was replaced by a superconducting false-vacuum formed by the Higgs mechanism of symmetry breaking. The ring-string emerged in this model as a narrow tube of the electromagnetic (EM) potential concentrated at the sharp border of the disklike source, similar to the well-known Nielsen-Olesen vortex string model in the Landau-Ginzburg theory [10].Recently, this model was generalized to a gravitating bag model [1], for which one of the known features is a flexibility and ability to create stringlike structures 1Principal peculiarity of the model consi...

The Dirac electron consistent with proper gravitational and electromagnetic field of the Kerr-Newman solution

“…Besides, it is formed by the system of chiral fields, when one of them depends on the Kerr angular coordinate and time. With respect to previous treatment [15,16], we obtain new very important feature of the DW source -formation of the DW-antiDW (breather) structure, which is very essential for the discussed here solutions of the Dirac equations.…”

“…In previous papers [15,16,17] we developed the line started by W. Israel [8], who suggested to truncate the second sheet of the Kerr geometry along the disk spanned by the Kerr singular ring. After analysis of the Israel source by Hamity [9], a modified disk-like source For r e = e 2 /2m disk is very thin, and r e /a = α corresponds to the fine structure const.…”

“…In the papers [15,16,17] we considered a generalization of the López model, in which the KN bubble is formed of the Higgs field, which is in a superconducting vacuum state. The thin shell of bubble is replaced by a domain-wall solution, which is described by the Landau-Ginzburg (LG) supersymmetric model of phase transition.…”

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“…However, a modification of the theory still occurs, and it is associated with the involvement of supersymmetry, i.e. with the additional inclusion of several chiral fields, forming the superconducting core of the Kerr spinning particle by the supersymmetric Higgs mechanism of spontaneous symmetry breaking [12][13][14][15]. In turn, supersymmetry has a similar property with respect to the gravitational field, which makes it possible to form a supersymmetric vacuum state that pushes the gravitational field out of the Compton zone of the particle.…”

“…As a result, a super-bag is formed inside the particle, inside which supersymmetry forms a vacuum state free from the gravitational and electromagnetic fields. By analogy with the well-known MIT-and SLAC-bag models, [2,3], formed as a non-perturbative solution of the Higgs model, the super-bag is formed on the basis of the supersymmetric Higgs model forming a flat internal space necessary for Compton core of quantum theory [12][13][14][15]. As a result of the conflict between Kerr gravity and quantum theory, two zones are formed: the outer classical (E) and the inner quantum (I), as well as the surface (S) separating these zones.…”