A nonstationary generalization of the Kerr congruence

Abstract

Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Electromagnetic and complex eikonal field distributions are naturally associated with the obtained congruence, with electric charge being necesssarily unit (``elementary''). We conjecture that the corresponding solution to the Einstein-Maxwell equations could describe the process of continious transition of the naked ringlike singularitiy into a rotating black hole and vice versa, under a particular current radius of the singular ring.Comment: 6 pages, twocolum

Wigner rotation and Thomas precession: geometric phases and related physical theories

“…[18] for applications). 2 Here and below,x denotes complex conjugation while we use ζ * = (ζ•, −ζ) for quaternion conjugation.…”

Twistor structures and boost-invariant solutions to field equations

“…(now Π (C) are two arbitrary functions of four twistor variables ξ, τ = Zξ) arises, in the framework of so-called algebrodynamical (AD) approach [4,5,6]. In fact, (3) represents the general solution of the conditions of biquaternionic B-differentiability [4,5] which are, in a sense, a natural generalization of the Cauchy-Riemann conditions in complex analysis.…”

“…(now Π (C) are two arbitrary functions of four twistor variables ξ, τ = Zξ) arises, in the framework of so-called algebrodynamical (AD) approach [4,5,6]. In fact, (3) represents the general solution of the conditions of biquaternionic B-differentiability [4,5] which are, in a sense, a natural generalization of the Cauchy-Riemann conditions in complex analysis. The form (3) reveals many "hidden" properties of the NSFC and, in particular, allows for a direct definition of a number of fundamental (both gauge and spinor) fields: complex Maxwell field, SL(2, C) Yang-Mills field, Weyl 2-spinor field and others [3].…”

Self-dual connections and the equations of fundamental fields in a Weyl–Cartan space

“…Such an approach, proposed in [1,2] (for more recent work, see [3]), is based on the differentiability conditions for functions of an algebraic (A) variable. The above conditions are just a generalization of the Cauchy-Riemann conditions in complex analysis to the case of an associative but noncommutative algebra A.…”

“…The physical fields associated with differentiable B-functions remain C-valued. Besides, the main class of solutions of (1) corresponds [2] to the case of the equality Ψ(Z) = F (Z) (or Φ(Z) = F (Z)); therefore, the B-differentiability conditions, which play the role of primary field equations, finally take the form…”