Twistor-beam excitations of black holes and prequantum Kerr-Schild geometry

Abstract

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.

Gravitating lepton bag model

“…The Kerr congruences are determined by the Kerr theorem, [21,46], which is formulated in twistor term on the auxiliary to KS metric (2) Minkowski space η µν . The first twistor component, Y plays also the role of a projective spinor coordinate (see details in Appendix and [16,46]). The Kerr theorem gives for the KN particle two solutions Y ± (x) which are connected by antipodal relation Y + = −1/Ȳ − and determine two antipodal congruences k + µν (x) and k − µν (x).…”

“…Regularization of the KN source does not remove this ring-string, but gives it a cut-off parameter (9), R = r e . It was shown in [10,11] and later specified in [44,45,46] that the EM excitations of the KN solution lead to appearance of traveling waves propagating along this ring-string. However, the light-like ring-string cannot be closed [47], since the points different by angular period, x µ (φ, t) and x µ (φ + 2π, t) should not coincide, and a peculiar point on the ring-string should make it open, forming a single quark-like endpoint.…”

Stringlike structures in Kerr-Schild geometry: The N=2 string, twistors, and the Calabi-Yau twofold

“…The string excitations are related with radiation and a recoil leading to non-stationarity of the solution. The exact non-stationary KS solutions are unknown, however the recoilless solutions were obtained in [24,30]. A recoil assumes a deviation of the 4-velocity δẋ µ L (τ )| τ − for the moments t > 0, which creates a difference between parameters A, B, C, determined for the retarded and advanced times τ − and τ + , resulting in two independent generating functions F ret (T A ) and F adv (T A ).…”

Instability of black hole horizon with respect to electromagnetic excitations

“…The long-term attack on the DKS equations performed in [4,5,8,9, 10] has led to the obtained in [11] time-dependent solutions which revealed a holographic structure of the fluctuating Kerr-Schild spacetimes and showed explicitly that electromagnetic radiation from a black-hole interacting with vacuum contains two components: a) a set of the singular beam pulses (determined by function ψ(Y, τ ),) propagating along the Kerr PNC and breaking the topology and stability of the horizon; b)the regularized radiative component (determined by γ reg (Y, τ )) which is smooth and, similar to that of the the Vaidya 'shining star' solution [6], determines evaporation of the black-hole,…”

“…The mysterious twosheetedness of the Kerr-Schild geometry plays principal role in the holographic black-hole spacetime [11], allowing one to consider action of the electromagnetic in-going vacuum as a time-dependent process of scattering. The obtained solutions describe excitations of electromagnetic beams on the Kerr-Schild background, the fine-grained fluctuations of the black-hole horizon, and the consistent back reaction of the beams to metric.…”