Kerr black holes as elementary particles

Arkani-Hamed, Nima; Huang, Yu-tin; O’Connell, Donal

doi:10.1007/JHEP01(2020)046

Title: Kerr black holes as elementary particles

Abstract

Long ago, Newman and Janis showed that a complex deformation z → z + ia of the Schwarzschild solution produces the Kerr solution. The underlying explanation for this relationship has remained obscure. The complex deformation has an electromagnetic counterpart: by shifting the Coloumb potential, we obtain the EM field of a certain rotating charge distribution which we term $ \sqrt{\mathrm{Kerr}} $. In this note, we identify the origin of this shift as arising from the exponentiation of spin operators for the recently defined “minimally coupled” three-particle amplitudes of spinning particles coupled to gravity, in the large- spin limit. We demonstrate this by studying the impulse imparted to a test particle in the background of the heavy spinning particle. We first consider the electromagnetic case, where the impulse due to $ \sqrt{\mathrm{Kerr}} $ is reproduced by a charged spinning particle; the shift of the Coloumb potential is matched to the exponentiated spin-factor appearing in the amplitude. The known impulse due to the Kerr black hole is then trivially derived from the gravitationally coupled spinning particle via the double copy.

Authors:

Arkani-Hamed, Nima ^[1]; Huang, Yu-tin ^[2]; O’Connell, Donal ^[3]

Inst. for Advanced Study, Princeton, NJ (United States)
National Taiwan Univ., Taipei (Taiwan); National Tsing Hua Univ., Hsinchu (Taiwan)
Univ. of Edinburgh, Scotland (United Kingdom)

Publication Date:: Wed Jan 08 00:00:00 EST 2020

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC); Simons Foundation; Science and Technology Facilities Council (STFC)

OSTI Identifier:: 1596096

Grant/Contract Number:: SC0009988; 106-2628-M-002-012-MY3

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Black Holes; Scattering Amplitudes

Citation Formats


                    Arkani-Hamed, Nima, Huang, Yu-tin, and O’Connell, Donal. Kerr black holes as elementary particles.  United States: N. p., 2020. 
Web.  doi:10.1007/JHEP01(2020)046.

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                    Arkani-Hamed, Nima, Huang, Yu-tin, & O’Connell, Donal. Kerr black holes as elementary particles.  United States.  https://doi.org/10.1007/JHEP01(2020)046

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                    Arkani-Hamed, Nima, Huang, Yu-tin, and O’Connell, Donal. Wed .  
"Kerr black holes as elementary particles".  United States.  https://doi.org/10.1007/JHEP01(2020)046.  https://www.osti.gov/servlets/purl/1596096.

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@article{osti_1596096,

  title        = {Kerr black holes as elementary particles},

  author       = {Arkani-Hamed, Nima and Huang, Yu-tin and O’Connell, Donal},

  abstractNote = {Long ago, Newman and Janis showed that a complex deformation z → z + ia of the Schwarzschild solution produces the Kerr solution. The underlying explanation for this relationship has remained obscure. The complex deformation has an electromagnetic counterpart: by shifting the Coloumb potential, we obtain the EM field of a certain rotating charge distribution which we term \( \sqrt{\mathrm{Kerr}} \). In this note, we identify the origin of this shift as arising from the exponentiation of spin operators for the recently defined “minimally coupled” three-particle amplitudes of spinning particles coupled to gravity, in the large- spin limit. We demonstrate this by studying the impulse imparted to a test particle in the background of the heavy spinning particle. We first consider the electromagnetic case, where the impulse due to \( \sqrt{\mathrm{Kerr}} \) is reproduced by a charged spinning particle; the shift of the Coloumb potential is matched to the exponentiated spin-factor appearing in the amplitude. The known impulse due to the Kerr black hole is then trivially derived from the gravitationally coupled spinning particle via the double copy.},

  doi          = {10.1007/JHEP01(2020)046},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 1,

  volume       = 2020,

  place        = {United States},

  year         = {Wed Jan 08 00:00:00 EST 2020},

  month        = {Wed Jan 08 00:00:00 EST 2020}

}

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Works referenced in this record:

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Kerr, Roy P.
Physical Review Letters, Vol. 11, Issue 5
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Guevara, Alfredo
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The simplest massive S-matrix: from minimal coupling to black holes
journal, April 2019

Chung, Ming-Zhi; Huang, Yu-tin; Kim, Jung-Wook
Journal of High Energy Physics, Vol. 2019, Issue 4
DOI: 10.1007/JHEP04(2019)156

Amplitudes, observables, and classical scattering
journal, February 2019

Kosower, David A.; Maybee, Ben; O’Connell, Donal
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Classical Physics and Quantum Loops
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Holstein, Barry R.; Donoghue, John F.
Physical Review Letters, Vol. 93, Issue 20
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Scattering of spinning black holes from exponentiated soft factors
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Guevara, Alfredo; Ochirov, Alexander; Vines, Justin
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Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
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Bern, Zvi; Cheung, Clifford; Roiban, Radu
Physical Review Letters, Vol. 122, Issue 20
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Black holes and the double copy
journal, December 2014

Monteiro, R.; O’Connell, D.; White, C. D.
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journal, June 1965

Newman, E. T.; Janis, A. I.
Journal of Mathematical Physics, Vol. 6, Issue 6
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Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
text, January 2019

Bern, Zvi; Cheung, Clifford; Roiban, Radu
ETH Zurich
DOI: 10.3929/ethz-b-000346888

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
text, January 2019

Foffa, Stefano; Porto Pereira, Rafael Alejandro; Rothstein, Ira
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2019-02862

Scattering of spinning black holes from exponentiated soft factors
text, January 2019

Alfredo, Guevara,; Alexander, Ochirov,; Justin, Vines,
ETH Zurich
DOI: 10.3929/ethz-b-000370487

The classical double copy for Taub-NUT spacetime
text, January 2015

Luna, A.; Monteiro, R.; O'Connell, D.
arXiv
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From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
text, January 2018

Cheung, Clifford; Rothstein, Ira Z.; Solon, Mikhail P.
arXiv
DOI: 10.48550/arxiv.1808.02489

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
text, January 2019

Foffa, Stefano; Porto, Rafael A.; Rothstein, Ira
arXiv
DOI: 10.48550/arxiv.1903.05118

Works referencing / citing this record:

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)
text, January 2020

Kälin, Gregor; Porto, Rafael A.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-01333

The Classical Double Copy of a Point Charge
text, January 2019

Kim, Kwangeon; Lee, Kanghoon; Monteiro, Ricardo
arXiv
DOI: 10.48550/arxiv.1912.02177

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Similar Records

Title: Kerr black holes as elementary particles

Abstract

Citation Formats

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics journal, September 1963

Kerr-Newman metric journal, January 2014

The classical double copy for Taub–NUT spacetime journal, November 2015

Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach. II. Renormalized Lagrangian journal, July 2019

Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering journal, April 2019

The simplest massive S-matrix: from minimal coupling to black holes journal, April 2019

Amplitudes, observables, and classical scattering journal, February 2019

Classical Physics and Quantum Loops journal, November 2004

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion journal, December 2018

Scattering of spinning black holes from exponentiated soft factors journal, September 2019

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order journal, May 2019

Black holes and the double copy journal, December 2014

Note on the Kerr Spinning‐Particle Metric journal, June 1965

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order text, January 2019

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian text, January 2019

Scattering of spinning black holes from exponentiated soft factors text, January 2019

The classical double copy for Taub-NUT spacetime text, January 2015

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion text, January 2018

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian text, January 2019

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist) text, January 2020

The Classical Double Copy of a Point Charge text, January 2019

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
journal, September 1963

Kerr-Newman metric
journal, January 2014

The classical double copy for Taub–NUT spacetime
journal, November 2015

Conservative dynamics of binary systems to fourth post-Newtonian order in the EFT approach. II. Renormalized Lagrangian
journal, July 2019

Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering
journal, April 2019

The simplest massive S-matrix: from minimal coupling to black holes
journal, April 2019

Amplitudes, observables, and classical scattering
journal, February 2019

Classical Physics and Quantum Loops
journal, November 2004

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
journal, December 2018

Scattering of spinning black holes from exponentiated soft factors
journal, September 2019

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
journal, May 2019

Black holes and the double copy
journal, December 2014

Note on the Kerr Spinning‐Particle Metric
journal, June 1965

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
text, January 2019

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
text, January 2019

Scattering of spinning black holes from exponentiated soft factors
text, January 2019

The classical double copy for Taub-NUT spacetime
text, January 2015

From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
text, January 2018

Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
text, January 2019

From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist)
text, January 2020

The Classical Double Copy of a Point Charge
text, January 2019