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.

Examples of non-commutative Hodge structures

We show that, under a condition called minimality, if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semidefinite Hermitian form, then the associated integrable twistor structure (or TERP structure, or noncommutative Hodge structure) is pure and polarized.

Relativistic angular momentum for asymptotically flat Einstein-Maxwell manifolds

Treating general relativity as a Yang-Mills theory based on Lorentz invariance of the second kind leads to the derivation of six spin currents, which are linear combinations of the Ricci rotation coefficients, together with a Gauss theorem for the integrated charges. For asymptotically flat Einstein-Maxwell manifolds these charges are calculated by performing two-surface integrals at future null infinity. The gauge dependence of these charges, which arises because the underlying group is non-Abelian, is removed by making a canonical alinement of the asymptotic frames of reference. The Lorentz generators then arise as a field in asymptotic spin space and defined on the set of all outgoing null cones, which is the carrier space of the B.M.S. group. In the absence of outgoing gravitational radiation the Lorentz generators transform under translations as a moment of momentum. However, the points about which moments are taken belong not to the original Riemannian manifold but rather to a four-parameter family of cones isomorphic to Minkowski space-time. From the angular momentum structure there arises a natural twistor structure. Points on the twistor and the centre of mass of the system are defined as world lines in the manifold of cones. The remainder of the paper is devoted to formulating physical laws in cone space. These include a Poynting’s theorem for the radiation of spin.