Kerr Singular Ring Research Articles

Source of the Kerr-Newman solution as a gravitating bag model: 50 years of the problem of the source of the Kerr solution

It is known that gravitational and electromagnetic fields of an electron are described by the ultra-extreme Kerr-Newman (KN) black hole solution with extremely high spin/mass ratio. This solution is singular and has a topological defect, the Kerr singular ring, which may be regularized by introducing the solitonic source based on the Higgs mechanism of symmetry breaking. The source represents a domain wall bubble interpolating between the flat region inside the bubble and external KN solution. It was shown recently that the source represents a supersymmetric bag model, and its structure is unambiguously determined by Bogomolnyi equations. The Dirac equation is embedded inside the bag consistently with twistor structure of the Kerr geometry, and acquires the mass from the Yukawa coupling with Higgs field. The KN bag turns out to be flexible, and for parameters of an electron, it takes the form of very thin disk with a circular string placed along sharp boundary of the disk. Excitation of this string by a traveling wave creates a circulating singular pole, indicating that the bag-like source of KN solution unifies the dressed and point-like electron in a single bag-string-quark system.

Kerr–Newman electron as spinning soliton

Measurable parameters of the electron indicate that its background should be described by the Kerr–Newman (KN) solution. The spin/mass ratio of the electron is extreme large and the black hole (BH) horizons disappear, opening a topological defect of space–time — the Kerr singular ring of Compton size, which may be interpreted as a closed fundamental string to low-energy string theory. The singular and two-sheeted structure of the corresponding Kerr space has to be regularized, and we consider the old problem of regularizing the source of the KN solution. As a development of the earlier Keres–Israel–Hamity–López model, we describe the model of smooth and regular source forming a gravitating and relativistically rotating soliton based on the chiral field model and the Higgs mechanism of broken symmetry. The model reveals some new remarkable properties: (1) the soliton forms a relativistically rotating bubble of Compton radius, which is filled by the oscillating Higgs field in a pseudo-vacuum state; (2) the boundary of the bubble forms a domain wall which interpolates between the internal flat background and the external exact KN solution; (3) the phase transition is provided by a system of chiral fields; (4) the vector potential of the external KN solution forms a closed Wilson loop which is quantized, giving rise to a quantized spin of the soliton and (5) the soliton is bordered by a closed string, which is a part of the general complex stringy structure.

Stringlike structures in the real and complex Kerr-Schild geometry

Four-dimensional Kerr-Schild (KS) geometry displays remarkable relationships with quantum world and theory of superstrings. In particular, the Kerr-Newman (KN) solution has gyromagnetic ratio g = 2, as that of the Dirac electron and represents a consistent background for gravitational and electromagnetic field of the electron. As a consequence of very big spin/mass ratio, black hole horizons disappear, exposing the naked Kerr singular ring. We consider four-decade history of development of this structure which took finally the form of a point-string-membrane-bubble complex which is reminiscent of the enhancon model of string/M-theory. A complex string obtained in the complex structure of the Kerr geometry gives an extra dimension to the world-sheet of the real Kerr string, forming a membrane by analogue with the string/M-theory unification. By analysis of the orientifold parity of the complex Kerr string, we obtain that the determined by the Kerr theorem principal null congruence of the Kerr geometry is described by a quartic equation in projective twistor space CP3, and therefore, it creates the known Calabi- Yau twofold (K3 surface) in twistor space of the 4d KS geometry. We connect it with N=2 superstring which has (complex) critical dimension two and may be embedded into complex KS geometry.

Stringlike structures in Kerr-Schild geometry: The N=2 string, twistors, and the Calabi-Yau twofold

The four-dimensional Kerr-Schild geometry contains two stringy structures. The first is the closed string formed by the Kerr singular ring, and the second is an open complex string obtained in the complex structure of the Kerr-Schild geometry. The real and complex Kerr strings together form a membrane source of the over-rotating Kerr-Newman solution without a horizon, a = J/m ≫ m. It was also recently found that the principal null congruence of the Kerr geometry is determined by the Kerr theorem as a quartic in the projective twistor space, which corresponds to an embedding of the Calabi-Yau twofold into the bulk of the Kerr geometry. We describe this embedding in detail and show that the four sheets of the twistorial K3 surface represent an analytic extension of the Kerr congruence created by antipodal involution.

Complex Structure of the Four-Dimensional Kerr Geometry: Stringy System, Kerr Theorem, and Calabi-Yau Twofold

The 4D Kerr geometry displays many wonderful relations with quantum world and, in particular, with superstring theory. The lightlike structure of fields near the Kerr singular ring is similar to the structure of Sen solution for a closed heterotic string. Another string, open and complex, appears in the complex representation of the Kerr geometry initiated by Newman. Combination of these strings forms a membrane source of the Kerr geometry which is parallel to the structure of M-theory. In this paper we give one more evidence of this relationship, emergence of the Calabi-Yau twofold (K3 surface) in twistorial structure of the Kerr geometry as a consequence of the Kerr theorem. Finally, we indicate that the Kerr stringy system may correspond to a complex embedding of the criticalN=2superstring.

Gravity beyond quantum theory: Electron as a closed heterotic string

The observable gravitational and electromagnetic parameters of an electron determine that its background should be the Kerr-Newman (KN) solution of the rotating black hole without horizons. This metric has a topological defect—the Kerr singular ring which, as we show, is a closed heterotic string of the Compton radius a = ħ/(2m). We show that the Dirac equation emerges as a consequence of the underlying KN gravity and string theory. Regularization of the KN solution leads to a model of gravitating soliton of the oscillon type, in which the closed heterotic string is positioned on the edge rim of a disklike vacuum bubble. It is suggested that the string-like core of the electron should be experimentally observable by the novel methods of the “Deeply Virtual (nonforward) Compton scattering”.

Gravitational strings beyond quantum theory: Electron as a closed heterotic string

The observable parameters of the electron indicate unambiguously that its gravitational background should be the Kerr-Newman solution without horizons. This background is not flat and has a non-trivial topology created by the Kerr singular ring. This ring was identified with a closed gravitational string. We discuss the relation of this string to the closed heterotic string of the low energy string theory and show that travelling waves along the KN string give rise to the Dirac theory of electron. Gravitational strings form a bridge between gravity and quantum theory, indicating a new way to consistent Quantum Gravity. We explain the pointlike experimental exhibition of the electron and argue that the predicted closed string may be observed by the novel experimental method of the "nonforward" Compton scattering.

Orientifold D-string in the source of the Kerr spinning particle

The model of spinning particle, based on the Kerr-Newman solution with |a}>>m, is discussed. It is shown that the Kerr singular ring can be considered as a string with an orientifold world-sheet. Orientifold adds to the Kerr ring an extra peculiar point, the fixed point of the world-sheet parity operator. It is shown that the Kerr string represents a new type of the string solutions and turns out to be an open D-string with joined ends which are in the circular light-like motion along the Kerr ring.

Regular sources of the Kerr-Schild class for rotating and nonrotating black hole solutions

A unified approach to regular interiors of black holes with smooth matter distributions in the core region is given. The approach is based on a class of Kerr-Schild metrics representing minimal deformations of the Kerr-Newman solution, and allows us to give a common treatment for (charged and uncharged) rotating and nonrotating black holes. It is shown that the requirement of smoothness of the source constrains the structure of the core region in many respects: in particular, for Schwarzschild holes a de Sitter core can be selected, which is surrounded by a smooth shell giving a leading contribution to the total mass of the source. In the rotating, noncharged case the source has a similar structure, taking the form of a (anisotropic and rotating) de Sitter--like core surrounded by a rotating elliptic shell. The Kerr singular ring is regularized by anisotropic matter rotating in the equatorial plane, so that the negative sheet of the Kerr geometry is absent. In the charged case the sources take the form of ``bags,'' which can have de Sitter or anti--de Sitter interiors and a smooth domain wall boundary, with a tangential stress providing charge confinement. The Arnowitt-Deser-Misner and Tolman relations are used to calculate the total mass of the sources.