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arxiv: 2507.18605 · v2 · submitted 2025-07-24 · ✦ hep-th · gr-qc

Graviton scattering on self-dual black holes

Tim Adamo , Giuseppe Bogna , Lionel Mason , Atul Sharma This is my paper

Pith reviewed 2026-05-19 02:23 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords graviton scatteringself-dual Taub-NUTtwistor theoryMHV amplitudesblack hole backgroundslinearised gravitycelestial symmetries
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0 comments X

The pith

Twistor theory produces an exact formula for MHV graviton scattering on self-dual Taub-NUT at any multiplicity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that linearised gravitational waves scattering on the self-dual Taub-NUT metric can be solved exactly thanks to integrability in the self-dual sector. Explicit quasi-momentum eigenstates are found, and these are used to build tree-level MHV amplitudes via a chiral sigma model whose target is the twistor space of the background. If this holds, it supplies a closed analytic expression for the amplitudes that remains valid for arbitrary numbers of gravitons and incorporates spin through a simple shift. The work also finds that holomorphic collinear splitting functions are identical to those in flat space, so the celestial symmetry algebra is undeformed. This matters because standard black-hole scattering calculations normally demand approximations or heavy numerics.

Core claim

Using a description of the self-dual Taub-NUT metric and its gravitons in terms of twistor theory, we obtain an explicit formula, exact in the background, for the tree-level maximal helicity violating graviton scattering amplitude at arbitrary multiplicity, with and without spin. This is obtained from the description of the MHV amplitudes in terms of the perturbation theory of a chiral sigma model whose target is the twistor space of the background. The incorporation of spin effects on these backgrounds is a straightforward application of the Newman-Janis shift. We also demonstrate that the holomorphic collinear splitting functions in the self-dual background are equal to those in flat space

What carries the argument

The chiral sigma model whose target is the twistor space of the self-dual Taub-NUT background, which generates the MHV amplitudes through its perturbation theory.

If this is right

  • The scattering amplitude remains exact in the background curvature with no need for perturbative expansion in the metric deviation.
  • The same formula applies to both spinless and spinning gravitons via the Newman-Janis shift.
  • Holomorphic collinear splitting functions are identical to their flat-space counterparts.
  • The celestial symmetry algebra therefore stays undeformed by the self-dual background.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method supplies a controlled analytic laboratory in which to examine how curvature modifies gravitational scattering before full numerical relativity on realistic black holes is attempted.
  • Persistence of flat-space collinear factors hints that certain features of celestial conformal symmetry may survive in curved self-dual geometries.
  • Low-multiplicity cases of the new formula could be cross-checked against independent perturbative calculations around the Taub-NUT metric to test consistency.

Load-bearing premise

The perturbation theory of the chiral sigma model on the twistor space of the background correctly reproduces the maximal helicity violating graviton amplitudes.

What would settle it

Direct computation of the three- or four-graviton MHV amplitude on the self-dual Taub-NUT background by solving the linearised Einstein equations in a different gauge or coordinate system and checking agreement with the sigma-model formula.

read the original abstract

The computation of gravitational wave scattering on black hole spacetimes is an extremely hard problem, typically requiring approximation schemes that either treat the black hole perturbatively or are only amenable to numerical techniques. In this paper, we consider linearised gravitational waves (or gravitons) scattering on the self-dual analogue of a black hole: namely, the self-dual Taub-NUT metric. Using the hidden integrability of the self-dual sector, we solve the linearised Einstein equations on these self-dual black hole backgrounds exactly in terms of simple, explicit quasi-momentum eigenstates. Using a description of the self-dual Taub-NUT metric and its gravitons in terms of twistor theory, we obtain an explicit formula, exact in the background, for the tree-level maximal helicity violating (MHV) graviton scattering amplitude at arbitrary multiplicity, with and without spin. This is obtained from the description of the MHV amplitudes in terms of the perturbation theory of a chiral sigma model whose target is the twistor space of the background. The incorporation of spin effects on these backgrounds is a straightforward application of the Newman-Janis shift. We also demonstrate that the holomorphic collinear splitting functions in the self-dual background are equal to those in flat space so that the celestial symmetry algebra is undeformed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims an exact tree-level MHV graviton scattering amplitude formula on self-dual Taub-NUT backgrounds at arbitrary multiplicity (with and without spin), obtained by solving the linearized Einstein equations exactly via integrability and quasi-momentum eigenstates, then extracting the amplitudes from perturbation theory of a chiral sigma model whose target is the twistor space of the background; it also shows that holomorphic collinear splitting functions remain identical to the flat-space case.

Significance. If the central formula holds, the result would be a notable advance for exact gravitational scattering computations in curved backgrounds, where approximations or numerics are usually required. The exact solution of the linearised equations and the explicit arbitrary-multiplicity formula are strengths, as is the demonstration that celestial symmetry is undeformed. The work builds on prior twistor and self-dual integrability literature but extends it non-trivially.

major comments (2)
  1. [paragraph on twistor description and sigma model] The central step asserting that the chiral sigma-model perturbation expansion on the twistor space of self-dual Taub-NUT directly yields the on-shell MHV graviton correlators (without additional curvature-induced corrections or redefinitions of external states) is presented as a straightforward extension of the flat-space case but is not re-derived or verified for the deformed holomorphic structure; this mapping is load-bearing for the explicit amplitude formula.
  2. [derivation of the MHV amplitude formula] A concrete low-multiplicity check (e.g., the 4-graviton MHV amplitude) against the flat-space limit or known results on the background would be needed to confirm that the quasi-momentum eigenstates and sigma-model vertices produce the correct gravitational amplitudes.
minor comments (2)
  1. Clarify the precise definition and normalization of the quasi-momentum eigenstates used to solve the linearized Einstein equations.
  2. Expand the brief mention of the Newman-Janis shift to include how it acts on the twistor data or external states.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped clarify several important aspects of the presentation. We address each major comment below and indicate the revisions made.

read point-by-point responses

  1. Referee: The central step asserting that the chiral sigma-model perturbation expansion on the twistor space of self-dual Taub-NUT directly yields the on-shell MHV graviton correlators (without additional curvature-induced corrections or redefinitions of external states) is presented as a straightforward extension of the flat-space case but is not re-derived or verified for the deformed holomorphic structure; this mapping is load-bearing for the explicit amplitude formula.

    Authors: We agree that the mapping merits a more explicit treatment in the deformed setting. The quasi-momentum eigenstates are constructed to solve the linearized Einstein equations exactly on the self-dual Taub-NUT background, and the sigma-model vertices are determined by the holomorphic structure of its twistor space. In the revised manuscript we have added a dedicated paragraph in Section 3 that re-derives the correspondence step by step, showing that the same dictionary between sigma-model correlators and on-shell MHV amplitudes continues to hold once the external states are taken to be these exact solutions; no additional curvature corrections or state redefinitions arise because the integrability of the self-dual sector is preserved. revision: yes

  2. Referee: A concrete low-multiplicity check (e.g., the 4-graviton MHV amplitude) against the flat-space limit or known results on the background would be needed to confirm that the quasi-momentum eigenstates and sigma-model vertices produce the correct gravitational amplitudes.

    Authors: We have performed the requested 4-graviton check in the flat-space limit and included the explicit result as a new consistency check in the revised text; it reproduces the standard MHV formula. On the curved background an independent cross-check is not presently available in the literature, but the construction guarantees correctness because the external wavefunctions satisfy the linearized equations exactly and the vertices follow from the twistor geometry. We have added a brief discussion of this point and of the flat-space reduction. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation applies established twistor integrability to new background

full rationale

The paper solves the linearized Einstein equations exactly via self-dual integrability and quasi-momentum eigenstates, then extracts MHV amplitudes from the perturbation expansion of a chiral sigma model on the twistor space of the self-dual Taub-NUT background. This mapping is an application of a pre-existing framework (standard in flat space) to a deformed geometry rather than a redefinition or fit of the target amplitudes themselves. No step reduces the claimed explicit formula to an input by construction, and self-citations (if present) support auxiliary results without bearing the central load. The result is therefore self-contained against external benchmarks in twistor theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the integrability of the self-dual sector and the equivalence between MHV amplitudes and perturbations of a chiral sigma model on twistor space; both are imported from prior literature rather than derived here.

axioms (2)
  • domain assumption The self-dual Taub-NUT metric admits hidden integrability that allows exact solutions of the linearised Einstein equations.
    Invoked to obtain quasi-momentum eigenstates and exact background solutions.
  • domain assumption MHV graviton amplitudes are generated by the perturbation theory of a chiral sigma model whose target is the twistor space of the background.
    Used to obtain the explicit amplitude formula.

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Works this paper leans on

158 extracted references · 158 canonical work pages · 29 internal anchors

  1. [1]

    S. W. Hawking,Particle Creation by Black Holes, Commun. Math. Phys.43 (1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)]

    work page 1975

  2. [2]

    S. W. Hawking,Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D14 (1976) 2460–2473

    work page 1976

  3. [3]

    Regge and J

    T. Regge and J. A. Wheeler,Stability of a Schwarzschild singularity, Phys. Rev. 108 (1957) 1063–1069

    work page 1957

  4. [4]

    F. J. Zerilli,Effective potential for even parity Regge-Wheeler gravitational perturbation equations, Phys. Rev. Lett.24 (1970) 737–738

    work page 1970

  5. [5]

    S. A. Teukolsky,Rotating black holes - separable wave equations for gravitational and electromagnetic perturbations, Phys. Rev. Lett.29 (1972) 1114–1118

    work page 1972

  6. [6]

    S. A. Teukolsky,Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations, Astrophys. J. 185 (1973) 635–647

    work page 1973

  7. [7]

    I. Y. Arefeva, L. D. Faddeev, and A. A. Slavnov,Generating Functional for the S Matrix in Gauge Theories, Theor. Math. Phys.21 (1975) 1165

    work page 1975

  8. [8]

    L. F. Abbott, M. T. Grisaru, and R. K. Schaefer,The Background Field Method and the S Matrix, Nucl. Phys. B229 (1983) 372–380

    work page 1983

  9. [9]

    Jevicki and C.-k

    A. Jevicki and C.-k. Lee,The S-Matrix Generating Functional and Effective Action, Phys. Rev. D 37 (1988) 1485. – 50 –

    work page 1988

  10. [10]

    A. A. Rosly and K. G. Selivanov,Gravitational SD perturbiner, hep-th/9710196

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    K. G. Selivanov,Post-classicism in Tree Amplitudes, in34th Rencontres de Moriond: Electroweak Interactions and Unified Theories, pp. 473–478, 1999.hep-th/9905128

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  12. [12]

    Ilderton and W

    A. Ilderton and W. Lindved,Scattering amplitudes and electromagnetic horizons, arXiv:2306.15475

    work page arXiv

  13. [13]

    Adamo, A

    T. Adamo, A. Cristofoli, A. Ilderton, and S. Klisch,Scattering amplitudes for self-force, Class. Quant. Grav.41 (2024), no. 6 065006, [arXiv:2307.00431]

    work page arXiv 2024

  14. [14]

    S. Kim, P. Kraus, R. Monten, and R. M. Myers,S-matrix path integral approach to symmetries and soft theorems, JHEP 10 (2023) 036, [arXiv:2307.12368]

    work page arXiv 2023

  15. [15]

    Cheung, J

    C. Cheung, J. Parra-Martinez, I. Z. Rothstein, N. Shah, and J. Wilson-Gerow,Effective Field Theory for Extreme Mass Ratio Binaries, Phys. Rev. Lett.132 (2024), no. 9 091402, [arXiv:2308.14832]

    work page arXiv 2024

  16. [16]

    Kosmopoulos and M

    D. Kosmopoulos and M. P. Solon,Gravitational self force from scattering amplitudes in curved space, JHEP 03 (2024) 125, [arXiv:2308.15304]

    work page arXiv 2024

  17. [17]

    Cheung, J

    C. Cheung, J. Parra-Martinez, I. Z. Rothstein, N. Shah, and J. Wilson-Gerow, Gravitational scattering and beyond from extreme mass ratio effective field theory, JHEP 10 (2024) 005, [arXiv:2406.14770]

    work page arXiv 2024

  18. [18]

    The scattering matrix approach for the quantum black hole, an overview

    G. ’t Hooft,The Scattering matrix approach for the quantum black hole: An Overview, Int. J. Mod. Phys. A11 (1996) 4623–4688, [gr-qc/9607022]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  19. [19]

    Unitary S Matrices With Long-Range Correlations and the Quantum Black Hole

    R. Akhoury,Unitary S Matrices With Long-Range Correlations and the Quantum Black Hole, JHEP 08 (2014) 169, [arXiv:1311.5613]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  20. [20]

    Betzios, N

    P. Betzios, N. Gaddam, and O. Papadoulaki,The Black Hole S-Matrix from Quantum Mechanics, JHEP 11 (2016) 131, [arXiv:1607.07885]

    work page arXiv 2016

  21. [21]

    Gaddam and N

    N. Gaddam and N. Groenenboom,2 → 2N scattering: Eikonalisation and the Page curve, JHEP 01 (2022) 146, [arXiv:2110.14673]

    work page arXiv 2022

  22. [22]

    He, A.-M

    T. He, A.-M. Raclariu, and K. M. Zurek,From shockwaves to the gravitational memory effect, JHEP 01 (2024) 006, [arXiv:2305.14411]

    work page arXiv 2024

  23. [23]

    Aoude, D

    R. Aoude, D. O’Connell, and M. Sergola,Amplitudes for Hawking Radiation, arXiv:2412.05267

    work page arXiv

  24. [24]

    Pasterski and A

    S. Pasterski and A. Puhm,Shifting spin on the celestial sphere, Phys. Rev. D104 (2021), no. 8 086020, [arXiv:2012.15694]

    work page arXiv 2021

  25. [25]

    Costello, N

    K. Costello, N. M. Paquette, and A. Sharma,Top-Down Holography in an Asymptotically Flat Spacetime, Phys. Rev. Lett.130 (2023), no. 6 061602, [arXiv:2208.14233]

    work page arXiv 2023

  26. [26]

    Costello, N

    K. Costello, N. M. Paquette, and A. Sharma,Burns space and holography, JHEP 10 (2023) 174, [arXiv:2306.00940]

    work page arXiv 2023

  27. [27]

    Fernandes, F.-L

    K. Fernandes, F.-L. Lin, and A. Mitra,Celestial eikonal amplitudes in the near-horizon region, Phys. Rev. D110 (2024), no. 12 126011, [arXiv:2310.03430]

    work page arXiv 2024

  28. [28]

    Adamo, W

    T. Adamo, W. Bu, P. Tourkine, and B. Zhu,Eikonal amplitudes on the celestial sphere, JHEP 10 (2024) 192, [arXiv:2405.15594]

    work page arXiv 2024

  29. [29]

    A. Luna, I. Nicholson, D. O’Connell, and C. D. White,Inelastic Black Hole Scattering from Charged Scalar Amplitudes, JHEP 03 (2018) 044, [arXiv:1711.03901]. – 51 –

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  30. [30]

    Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings

    J. Vines,Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings, Class. Quant. Grav.35 (2018), no. 8 084002, [arXiv:1709.06016]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  31. [31]

    Guevara, A

    A. Guevara, A. Ochirov, and J. Vines,Scattering of Spinning Black Holes from Exponentiated Soft Factors, JHEP 09 (2019) 056, [arXiv:1812.06895]

    work page arXiv 2019

  32. [32]

    Arkani-Hamed, Y.-t

    N. Arkani-Hamed, Y.-t. Huang, and D. O’Connell,Kerr black holes as elementary particles, JHEP 01 (2020) 046, [arXiv:1906.10100]

    work page arXiv 2020

  33. [33]

    Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines,Scattering in black hole backgrounds and higher-spin amplitudes. Part I, JHEP 03 (2023) 136, [arXiv:2107.10179]

    work page arXiv 2023

  34. [34]

    M. V. S. Saketh and J. Vines,Scattering of gravitational waves off spinning compact objects with an effective worldline theory, Phys. Rev. D106 (2022), no. 12 124026, [arXiv:2208.03170]

    work page arXiv 2022

  35. [35]

    Y. F. Bautista, A. Guevara, C. Kavanagh, and J. Vines,Scattering in black hole backgrounds and higher-spin amplitudes. Part II, JHEP 05 (2023) 211, [arXiv:2212.07965]

    work page arXiv 2023

  36. [36]

    Gonzo, T

    R. Gonzo, T. McLoughlin, and A. Puhm,Celestial holography on Kerr-Schild backgrounds, JHEP 10 (2022) 073, [arXiv:2207.13719]

    work page arXiv 2022

  37. [37]

    Cangemi, M

    L. Cangemi, M. Chiodaroli, H. Johansson, A. Ochirov, P. Pichini, and E. Skvortsov, Compton Amplitude for Rotating Black Hole from QFT, Phys. Rev. Lett.133 (2024), no. 7 071601, [arXiv:2312.14913]

    work page arXiv 2024

  38. [38]

    Bohnenblust, L

    L. Bohnenblust, L. Cangemi, H. Johansson, and P. Pichini,Binary Kerr black-hole scattering at 2PM from quantum higher-spin Compton, arXiv:2410.23271

    work page arXiv

  39. [39]

    A. H. Taub,Empty space-times admitting a three parameter group of motions, Annals Math. 53 (1951) 472–490

    work page 1951

  40. [40]

    Newman, L

    E. Newman, L. Tamburino, and T. Unti,Empty space generalization of the Schwarzschild metric, J. Math. Phys.4 (1963) 915

    work page 1963

  41. [41]

    C. W. Misner,The Flatter regions of Newman, Unti and Tamburino’s generalized Schwarzschild space, J. Math. Phys.4 (1963) 924–938

    work page 1963

  42. [42]

    S. W. Hawking,Gravitational Instantons, Phys. Lett. A60 (1977) 81

    work page 1977

  43. [43]

    G. W. Gibbons and S. W. Hawking,Gravitational Multi-Instantons, Phys. Lett. B78 (1978) 430

    work page 1978

  44. [44]

    G. W. Gibbons and S. W. Hawking,Classification of Gravitational Instanton Symmetries, Commun. Math. Phys.66 (1979) 291–310

    work page 1979

  45. [45]

    Penrose,Nonlinear gravitons and curved twistor theory, Gen

    R. Penrose,Nonlinear gravitons and curved twistor theory, Gen. Rel. Grav.7 (1976) 31–52

    work page 1976

  46. [46]

    Crawley, A

    E. Crawley, A. Guevara, E. Himwich, and A. Strominger,Self-dual black holes in celestial holography, JHEP 09 (2023) 109, [arXiv:2302.06661]

    work page arXiv 2023

  47. [47]

    Guevara and U

    A. Guevara and U. Kol,Self Dual Black Holes as the Hydrogen Atom, arXiv:2311.07933

    work page arXiv

  48. [48]

    Araneda,Teukolsky equations, twistor functions, and conformally self-dual spaces, arXiv:2407.10939

    B. Araneda,Teukolsky equations, twistor functions, and conformally self-dual spaces, arXiv:2407.10939

    work page arXiv

  49. [49]

    Guevara, U

    A. Guevara, U. Kol, and H. Tran,An Exact Black Hole Scattering Amplitude, arXiv:2412.19627

    work page arXiv

  50. [50]

    Adamo, G

    T. Adamo, G. Bogna, L. Mason, and A. Sharma,Scattering on self-dual Taub-NUT, Class. – 52 – Quant. Grav. 41 (2024), no. 1 015030, [arXiv:2309.03834]

    work page arXiv 2024

  51. [51]

    L. J. Mason and D. Skinner,Gravity, Twistors and the MHV Formalism, Commun. Math. Phys. 294 (2010) 827–862, [arXiv:0808.3907]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  52. [52]

    Adamo, L

    T. Adamo, L. Mason, and A. Sharma,Twistor sigma models for quaternionic geometry and graviton scattering, Adv. Theor. Math. Phys.27 (2023), no. 3 623–681, [arXiv:2103.16984]

    work page arXiv 2023

  53. [53]

    Miller,Proof of the graviton MHV formula using Plebanski’s second heavenly equation, arXiv:2408.11139

    N. Miller,Proof of the graviton MHV formula using Plebanski’s second heavenly equation, arXiv:2408.11139

    work page arXiv

  54. [54]

    Guevara, E

    A. Guevara, E. Himwich, and N. Miller,Generating Hodges’ Graviton MHV Formula with an Lw1+∞ Ward Identity, arXiv:2506.05460

    work page arXiv

  55. [55]

    A simple formula for gravitational MHV amplitudes

    A. Hodges,A simple formula for gravitational MHV amplitudes, arXiv:1204.1930

    work page internal anchor Pith review Pith/arXiv arXiv 1930

  56. [56]

    E. T. Newman and A. I. Janis,Note on the Kerr spinning particle metric, J. Math. Phys.6 (1965) 915–917

    work page 1965

  57. [57]

    Lectures on twistor theory

    T. Adamo,Lectures on twistor theory, PoS Modave2017 (2018) 003, [arXiv:1712.02196]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Newman and R

    E. Newman and R. Penrose,An Approach to gravitational radiation by a method of spin coefficients, J. Math. Phys.3 (1962) 566–578

    work page 1962

  59. [59]

    Kinnersley,Type D Vacuum Metrics, J

    W. Kinnersley,Type D Vacuum Metrics, J. Math. Phys.10 (1969) 1195–1203

    work page 1969

  60. [60]

    Crawley, A

    E. Crawley, A. Guevara, N. Miller, and A. Strominger,Black holes in Klein space, JHEP 10 (2022) 135, [arXiv:2112.03954]

    work page arXiv 2022

  61. [61]

    D. A. Easson and M. W. Pezzelle,Kleinian black holes, Phys. Rev. D109 (2024), no. 4 044007, [arXiv:2312.00879]

    work page arXiv 2024

  62. [62]

    LeBrun,Complete Ricci-flat Kähler metrics onCn need not be flat, inProc

    C. LeBrun,Complete Ricci-flat Kähler metrics onCn need not be flat, inProc. Symp. Pure Math, vol. 52, pp. 297–304, 1991

    work page 1991

  63. [63]

    J. F. Plebanski,Some solutions of complex Einstein equations, J. Math. Phys.16 (1975) 2395–2402

    work page 1975

  64. [64]

    C. J. Talbot,Newman-Penrose approach to twisting degenerate metrics, Commun. Math. Phys. 13 (1969), no. 1 45–61

    work page 1969

  65. [65]

    S. P. Drake and P. Szekeres,Uniqueness of the Newman-Janis algorithm in generating the Kerr-Newman metric, Gen. Rel. Grav.32 (2000) 445–458, [gr-qc/9807001]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  66. [66]

    A. J. Keane,An extension of the Newman-Janis algorithm, Class. Quant. Grav.31 (2014) 155003, [arXiv:1407.4478]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  67. [67]

    Janis-Newman algorithm: simplifications and gauge field transformation

    H. Erbin,Janis–Newman algorithm: simplifications and gauge field transformation, Gen. Rel. Grav.47 (2015) 19, [arXiv:1410.2602]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  68. [68]

    The Kerr-Newman metric: A Review

    T. Adamo and E. T. Newman,The Kerr-Newman metric: A Review, Scholarpedia 9 (2014) 31791, [arXiv:1410.6626]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  69. [69]

    Deciphering and generalizing Demianski-Janis-Newman algorithm

    H. Erbin,Deciphering and generalizing Demiański–Janis–Newman algorithm, Gen. Rel. Grav. 48 (2016), no. 5 56, [arXiv:1411.2909]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  70. [70]

    Janis-Newman algorithm: generating rotating and NUT charged black holes

    H. Erbin,Janis-Newman algorithm: generating rotating and NUT charged black holes, Universe 3 (2017), no. 1 19, [arXiv:1701.00037]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  71. [71]

    Cartesian Kerr-Schild variation on the Newman-Janis ansatz

    D. Rajan and M. Visser,Cartesian Kerr–Schild variation on the Newman–Janis trick, Int. J. Mod. Phys. D26 (2017), no. 14 1750167, [arXiv:1601.03532]. – 53 –

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  72. [72]

    W. T. Emond, Y.-T. Huang, U. Kol, N. Moynihan, and D. O’Connell,Amplitudes from Coulomb to Kerr-Taub-NUT, JHEP 05 (2022) 055, [arXiv:2010.07861]

    work page arXiv 2022

  73. [73]

    Beltracchi and P

    P. Beltracchi and P. Gondolo,Physical interpretation of Newman-Janis rotating systems. I. A unique family of Kerr-Schild systems, Phys. Rev. D104 (2021), no. 12 124066, [arXiv:2104.02255]

    work page arXiv 2021

  74. [74]

    Kim,Newman-Janis Algorithm from Taub-NUT Instantons, arXiv:2412.19611

    J.-H. Kim,Newman-Janis Algorithm from Taub-NUT Instantons, arXiv:2412.19611

    work page arXiv

  75. [75]

    Carter,Hamilton-Jacobi and Schrodinger separable solutions of Einstein’s equations, Commun

    B. Carter,Hamilton-Jacobi and Schrodinger separable solutions of Einstein’s equations, Commun. Math. Phys.10 (1968), no. 4 280–310

    work page 1968

  76. [76]

    Carter,Global structure of the Kerr family of gravitational fields, Phys

    B. Carter,Global structure of the Kerr family of gravitational fields, Phys. Rev. 174 (1968) 1559–1571

    work page 1968

  77. [77]

    J. G. Miller,Global analysis of the Kerr-Taub-NUT metric, J. Math. Phys.14 (1973), no. 4 486

    work page 1973

  78. [78]

    Penrose and W

    R. Penrose and W. Rindler,Spinors and Space-Time, vol. 1 ofCambridge Monographs on Mathematical Physics. Cambridge Univ. Press, Cambridge, UK, 1984

    work page 1984

  79. [79]

    Walker and R

    M. Walker and R. Penrose,On quadratic first integrals of the geodesic equations for type

    work page

  80. [80]

    spacetimes, Commun. Math. Phys.18 (1970) 265–274

    work page 1970

Showing first 80 references.