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” threeparticle 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 spinfactor 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:

 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:
 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; 1062628M002012MY3
 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 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Black Holes; Scattering Amplitudes
Citation Formats
ArkaniHamed, Nima, Huang, Yutin, and O’Connell, Donal. Kerr black holes as elementary particles. United States: N. p., 2020.
Web. doi:10.1007/JHEP01(2020)046.
ArkaniHamed, Nima, Huang, Yutin, & O’Connell, Donal. Kerr black holes as elementary particles. United States. https://doi.org/10.1007/JHEP01(2020)046
ArkaniHamed, Nima, Huang, Yutin, 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 = {ArkaniHamed, Nima and Huang, Yutin 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” threeparticle 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 spinfactor 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}
}
Web of Science
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Works referencing / citing this record:
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