Renormalization by gravity and the Kerr spinning particle

On the basis of the Kerr spinning particle, we show that the mass renormalization is perfectly performed by gravity for an arbitrary distribution of source matter. A smooth regularization of the Kerr-Newman solution is considered, leading to a source in the form of a rotating bag filled by a false vacuum. It is shown that gravity controls the phase transition to an AdS or dS false vacuum state inside the bag, providing the mass balance.Comment: 9 pages, 2 figure

The Kerr theorem and multiparticle Kerr-Schild solutions

We discuss and prove an extended version of the Kerr theorem which allows one to construct exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of twistor variables. The exact multiparticle Kerr-Schild solutions are obtained from generating function of the form $F=\prod_i^k F_i,$ where $F_i$ are partial generating functions for the spinning particles $i=1...k$. Solutions have an unusual multi-sheeted structure. Twistorial structures of the i-th and j-th particles do not feel each other, forming a type of its internal space. Gravitational and electromagnetic interaction of the particles occurs via the light-like singular twistor lines. As a result, each particle turns out to be `dressed' by singular pp-strings connecting it to other particles. We argue that this solution may have a relation to quantum theory and to quantum gravity.Comment: 13 pages, 4 figures, revtex. Expressions for electromagnetic field are correcte

Regularized Kerr-Newman Solution as a Gravitating Soliton

The charged, spinning and gravitating soliton is realized as a regular solution of the Kerr-Newman field coupled with a chiral Higgs model. A regular core of the solution is formed by a domain wall bubble interpolating between the external Kerr-Newman solution and a flat superconducting interior. An internal electromagnetic (em) field is expelled to the boundary of the bubble by the Higgs field. The solution reveals two new peculiarities: (i) the Higgs field is oscillating, similar to the known oscillon models, (ii) the em field forms on the edge of the bubble a Wilson loop, resulting in quantization of the total angular momentum.Comment: Final published version, essential corrections, title changed, 8 pages, one fi

Complex Kerr Geometry, Twistors and the Dirac Electron

The Kerr-Newman spinning particle displays some remarkable relations to the Dirac electron and has a reach spinor structure which is based on a twistorial description of the Kerr congruence determined by the Kerr theorem. We consider the relation between this spinor-twistorial structure and spinors of the Dirac equation, and show that the Dirac equation may naturally be incorporated into Kerr-Schild formalism as a master equation controlling the twistorial structure of Kerr geometry. As a result, the Dirac electron acquires an extended space-time structure having clear coordinate description with natural incorporation of a gravitational field. The relation between the Dirac wave function and Kerr geometry is realized via a chain of links: {\it Dirac wave function $\Rightarrow$ Complex Kerr-Newman Source $\Rightarrow$ Kerr Theorem $\Rightarrow$ Real Kerr geometry.} As a result, the wave function acquires the role of an ``order parameter'' which controls spin, dynamics, and twistorial polarization of Kerr-Newman space-time.Comment: 12 pages, 3 figs. Talk at the conference QFEXT'0

Gravity vs. Quantum theory: Is electron really pointlike?

The observable gravitational and electromagnetic parameters of an electron: mass $m$, spin $J=\hbar/2$, charge $e$ and magnetic moment $ea = e\hbar /(2m)$ indicate unambiguously that the electron should had the Kerr-Newman background geometry -- exact solution of the Einstein-Maxwell gravity for a charged and rotating black hole. Contrary to the widespread opinion that gravity plays essential role only on the Planck scales, the Kerr-Newman gravity displays a new dimensional parameter $a =\hbar/(2m),$ which for parameters of an electron corresponds to the Compton wavelength and turns out to be very far from the Planck scale. Extremely large spin of the electron with respect to its mass produces the Kerr geometry without horizon, which displays very essential topological changes at the Compton distance resulting in a two-fold structure of the electron background. The corresponding gravitational and electromagnetic fields of the electron are concentrated near the Kerr ring, forming a sort of a closed string, structure of which is close to the described by Sen heterotic string. The indicated by Gravity stringlike structure of the electron contradicts to the statements of Quantum theory that electron is pointlike and structureless. However, it confirms the peculiar role of the Compton zone of the "dressed" electron and matches with the known limit of the localization of the Dirac electron. We discuss the relation of the Kerr string with the low energy string theory and with the Dirac theory of electron and suggest that the predicted by the Kerr-Newman gravity closed string in the core of the electron, should be experimentally observable by the novel regime of the high energy scattering -- the Deeply Virtual (or "nonforward")Compton Scattering".Comment: 15 pages,6 figures, proceedings of the conference QTS7, v.2 reference correcte

Twistor-Beam Excitations of Black-Holes and Prequantum Kerr-Schild Geometry

Exact Kerr-Schild (KS) solutions for electromagnetic excitations of black-holes, have the form of singular beams supported on twistor lines of the KS geometry. These beams have a very strong back-reaction on the metric and horizon and create a fluctuating KS geometry occupying an intermediate position between the classical and quantum gravities. We consider the Kerr theorem, which determines the twistor structure of the KS geometry and the corresponding holographic prequantum space-time adapted to subsequent quantum treatment.Comment: 7 pages, 3 Figures. Published version. Talk at the SFT09 conference, MIAN (Steklov Math. Institute), April 200

Structure of Spinning Particle Suggested by Gravity, Supergravity and Low Energy String Theory

The structure of spinning particle suggested by the rotating Kerr-Newman (black hole) solution, super-Kerr-Newman solution and the Kerr-Sen solution to low energy string theory is considered. Main peculiarities of the Kerr spinning particle are discussed: a vortex of twisting principal null congruence, singular ring and the Kerr source representing a rotating relativistic disk of the Compton size. A few stringy structures can be found in the real and complex Kerr geometry. Low-energy string theory predicts the existence of a heterotic string placed on the sharp boundary of this disk. The obtained recently supergeneralization of the Kerr-Newman solution suggests the existence of extra axial singular line and fermionic traveling waves concentrating near these singularities. We discuss briefly a possibility of experimental test of these predictions.Comment: Latex, 8 pages, talk at the International Workshop Spin'99, Prague, 5-11 September, 199

Rotating Black Hole, Twistor-String and Spinning Particle

We discuss basic features of the model of spinning particle based on the Kerr solution. It contains a very nontrivial {\it real} stringy structure consisting of the Kerr circular string and an axial stringy system. We consider also the complex and twistorial structures of the Kerr geometry and show that there is a {\it complex} twistor-string built of the complex N=2 chiral string with a twistorial $(x,\theta)$ structure. By imbedding into the real Minkowski $\bf M^4$, the N=2 supersymmetry is partially broken and string acquires the open ends. Orientifolding this string, we identify the chiral and antichiral structures. Target space of this string is equivalent to the Witten's `diagonal' of the $\bf CP^3\times CP^{*3}.$Comment: 19 p. 4 figures, extended version of hep-th/0412065, based on the talk given at the Conference `Symmetries and Spin'(SPIN-Praha-2004) July 200

SOME PROPERTIES OF THE KERR SOLUTION TO LOW ENERGY STRING THEORY

The Kerr solution to axidilaton gravity is analyzed in the Debney--Kerr--Schild formalism. It is shown that the Kerr principal null congruence retains its property to be geodesic and shear free, however, the axidilatonic Kerr solution is not algebraically special. A limiting form of this solution is considered near the ring-like Kerr singularity. This limiting solution coincides with the field around a fundamental heterotic string obtained by Sen.Comment: 14 pages., LaTe

The Newman-Janis Algorithm, Rotating Solutions and Einstein-Born-Infeld Black Holes

A new metric is obtained by applying a complex coordinate trans- formation to the static metric of the self-gravitating Born-Infeld monopole. The behaviour of the new metric is typical of a rotating charged source, but this source is not a spherically symmetric Born-Infeld monopole with rotation. We show that the structure of the energy-momentum tensor obtained with this new metric does not correspond to the typical structure of the energy momentum tensor of Einstein-Born-Infeld theory induced by a rotating spherically symmetric source. This also show, that the complex coordinate transformations have the interpretation given by Newman and Janis only in space-time solutions with linear sources