Complex structure of Kerr geometry and rotating  photon rocket  solutions

Abstract

In the frame of the Kerr-Schild approach, we obtain a generalization of the Kerr solution to a nonstationary case corresponding to a rotating source moving with arbitrary acceleration. Similar to the Kerr solution, the solutions obtained have the geodesic and shear free principal null congruence. The current parameters of the solutions are determined by a complex retarded-time construction via a given complex worldline of source. The real part of the complex worldline defines the values of the boost and acceleration while the imaginary part controls the rotation. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. The solutions obtained generalize to the rotating case the known Kinnersley class of the "photon rocket" solutions.

Twistorial analyticity and three stringy systems of the Kerr spinning particle

“…For the reader convenience we describe here briefly the necessary details of the real and complex structures of the Kerr geometry. For more details see [7,8,23]. …”

“…In the Kerr solution function F is quadratic in Y , and the equation F = 0 and the system F (Y ) = dF (Y )/dY = 0 can be explicitly resolved [23] yielding the structure of the Kerr PNC and the Kerr singular ring shown in the Fig.2. The Kerr singular ring is the branch line of the Kerr space on two sheets: 'positive' (r > 0) and 'negative' (r < 0) ones, so the Kerr PNC propagates from the 'negative' sheet onto 'positive' one through the disk spanned by the Kerr ring.…”

“…The Kerr singular ring is the branch line of the Kerr space on two sheets: 'positive' (r > 0) and 'negative' (r < 0) ones, so the Kerr PNC propagates from the 'negative' sheet onto 'positive' one through the disk spanned by the Kerr ring. Since the PNC determines a flow of radiation (in radiative solutions), one sees that outgoing radiation is compensated by an ingoing flow on the negative sheet, so the negative sheet acquires the interpretation as a list of advanced fields which are related to the vacuum zero point fields [11,23,12]. In this interpretation, the wave excitations can be treated as a result of resonance of a zero point field on the Kerr ring, in the spirit of the semiclassical Casimir effect.…”

“…It turns out that this is provided by the holomorphy and orientifold structure of the third, complex string of the Kerr geometry [7]. The complex representation of the Kerr geometry [23,7,8,10] is generated by a complex world line X µ 0 (τ ) ∈ CM 4 , where τ = t 0 + iσ is a complex time parameter. In the stationary Kerr case X µ 0 (τ ) = (τ, 0, 0, ia).…”

Rotating black hole, twistor-string and spinning particle

“…The fields change directions and signs on the negative sheet. The negative sheet acquires an interpretation of the sheet of advanced fields which may be related to the vacuum zero point field [13,14,15]. The particles, strings or twistors disappear in (emerge from) a mirror world passing through the Kerr ring (see Fig.…”