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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:
 [1];  [2];  [3]
  1. Inst. for Advanced Study, Princeton, NJ (United States)
  2. National Taiwan Univ., Taipei (Taiwan); National Tsing Hua Univ., Hsinchu (Taiwan)
  3. Univ. of Edinburgh, Scotland (United Kingdom)
Publication Date:
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.
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
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.
@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 = {2020},
month = {1}
}

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Works referenced in this record:

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

  • 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
  • Journal of High Energy Physics, Vol. 2019, Issue 2
  • DOI: 10.1007/JHEP02(2019)137

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

  • Guevara, Alfredo; Ochirov, Alexander; Vines, Justin
  • Journal of High Energy Physics, Vol. 2019, Issue 9
  • DOI: 10.1007/JHEP09(2019)056

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

  • Monteiro, R.; O’Connell, D.; White, C. D.
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)056

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

  • Newman, E. T.; Janis, A. I.
  • Journal of Mathematical Physics, Vol. 6, Issue 6
  • DOI: 10.1063/1.1704350

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


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


Works referencing / citing this record:

The classical double copy of a point charge
journal, February 2020

  • Kim, Kwangeon; Lee, Kanghoon; Monteiro, Ricardo
  • Journal of High Energy Physics, Vol. 2020, Issue 2
  • DOI: 10.1007/jhep02(2020)046

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


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