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Newman-Janis Algorithm from Taub-NUT Instantons

Joon-Hwi Kim

TL;DR

This work provides a principled derivation of the Kerr metric by showing it arises as the nonlinear superposition of self-dual and anti-self-dual Taub–NUT instantons, within the KS double-copy framework. By factorizing the ring singularity into two imaginarily centered instantons and applying a nonlinear superposition theorem for canonical null vector fields, the authors derive Kerr (and charged generalizations) as exact solutions, not as coordinate tricks. The approach clarifies the historical Newman–Janis algorithm by linking it directly to two-instanton physics and extends naturally to Kerr–Newman and the five-parameter Plebański–Demiański family. The work connects gravitational instanton structure, chiral dyons, and modern scattering/perturbation theory perspectives, with potential implications for rotating black hole physics and amplitude methods.

Abstract

It is shown that the Kerr metric represents the nonlinear superposition of self-dual and anti-self-dual Taub-NUT instantons. This promotes the Newman-Janis algorithm to a rigorous derivation of the Kerr metric with a definite physical origin. In the same way, the Kerr-Newman and charged Kerr-Taub-NUT solutions are systems of Taub-NUT instantons and chiral dyons.

Newman-Janis Algorithm from Taub-NUT Instantons

TL;DR

This work provides a principled derivation of the Kerr metric by showing it arises as the nonlinear superposition of self-dual and anti-self-dual Taub–NUT instantons, within the KS double-copy framework. By factorizing the ring singularity into two imaginarily centered instantons and applying a nonlinear superposition theorem for canonical null vector fields, the authors derive Kerr (and charged generalizations) as exact solutions, not as coordinate tricks. The approach clarifies the historical Newman–Janis algorithm by linking it directly to two-instanton physics and extends naturally to Kerr–Newman and the five-parameter Plebański–Demiański family. The work connects gravitational instanton structure, chiral dyons, and modern scattering/perturbation theory perspectives, with potential implications for rotating black hole physics and amplitude methods.

Abstract

It is shown that the Kerr metric represents the nonlinear superposition of self-dual and anti-self-dual Taub-NUT instantons. This promotes the Newman-Janis algorithm to a rigorous derivation of the Kerr metric with a definite physical origin. In the same way, the Kerr-Newman and charged Kerr-Taub-NUT solutions are systems of Taub-NUT instantons and chiral dyons.
Paper Structure (9 sections, 27 equations, 4 figures)

This paper contains 9 sections, 27 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Intuition and Overview
  3. Factorization of Kerr
  4. Nonlinear Superposition Theorem
  5. Derivation of Kerr Metric
  6. NJA Deciphered
  7. NJA for Charged Kerr-Taub-NUT
  8. Summary
  9. Acknowledgements

Figures (4)

  • Figure 1: In electromagnetism, a current loop behaves like a pair of opposite monopoles: Ampèrian and Gilbertian dipoles griffiths3ed. This letter reveals a gravitational version of this duality.
  • Figure 2: The ring singularity of Kerr black hole factorizes into a pair of SD and ASD Taub-NUT instantons.
  • Figure 3: In an accurate sense, the NJA first decomposed a Schwarzschild black hole into SD () and ASD () Taub-NUT instantons and then moved them independently.
  • Figure 4: Implementing pure mass (left) and magnetic mass (right) with Taub-NUT instantons.