Accelerating electromagnetic magic field from the C-metric

Abstract

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges

Point particles and Appell’s solutions on the axis of a Kerr black hole for an arbitrary spin in terms of the Debye potentials

“…We found its generalization to uniformly accelerated case, i.e. the G → 0 limit of the C-metric, in [42]. The Debye potential for a point-like particle (84) and (53) has its location encoded in parameters r 0 and r 0 , θ 0 , ϕ 0 , respectively.…”

Classical Limits of Boost-Rotation Symmetric Spacetimes

“…Then in the limit the hyperbola turns into the parabola. Before performing the limit λ → 0 it is crucial to make the substitution (5). We can calculate the nontrivial components of affine connection and find Γ a tt = lim…”

Rotating charged black holes accelerated by an electric field

“…3 The same as in Eqs. (10), (11) in [20], i.e., t → K(1 + a 2 A 2 )t and ϕ → ϕ − aAK −1 (1 + a 2 A 2 )t. of x and y coordinates in (3) as follows: y ∈ ξ 2 , ξ 3 for quadrant I (see Fig. 1), y ∈ ξ 3 , ξ 4 for quadrant II and x ∈ ξ 3 , ξ 4 .…”

“…Then A is acceleration with respect to the flat background. For a = 0, the source is a rotating disc with complicated structure (see [20] for details).…”