The Kerr two-twistor particle

TL;DR

The paper develops an all-orders worldline action for a Kerr black hole in curved spacetime within a curved massive twistor framework, treating spin as an imaginary deviation via the generator $N$ and the almost complex structure $J$ to realize Newman–Janis shifts to all orders. It introduces curved massive correspondence space $ ext{K}$ and curved massive twistor space $ ext{MT}$, derives a self-dual (heaven) limit in which the dynamics localize on a holomorphic worldline $z^ ext{μ'}$, and constructs a Googly/Kerr action that couples both self-dual and anti-self-dual sectors through holomorphic data. The framework yields a physical interpretation of Kerr as a self-dual/anti-self-dual dyon system connected by Misner strings (Taub–NUT instantons) and provides a path toward curved massive twistor theory via deformed massive incidence relations. Together, these results deliver a geometric, all-orders description of Kerr couplings to curvature with potential implications for gravitational scattering and post-Minkowskian gravity.

Abstract

An all-orders worldline effective action for Kerr black hole is achieved in twistor particle theory.

Figures (8)

• Figure 1: Flat massive twistor theory.
• Figure 2: The "${\iota}_N d / J$ sequence" for Kerr. A tree of one-forms emanates from the scalar-particle symplectic potential, $p_m\space e^m$.
• Figure 3: Gilbert-Ampère duality.
• Figure 4: Curved massive twistor theory.
• Figure 5: The ring singularity of Kerr black hole turns into a pair of self-dual and anti-self-dual Taub-NUT instantons.