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Title: Isometries and the double copy

Abstract

In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell’s equations. However, it is well known that the vacuum Einstein equations imply that the Kerr-Schild vector is geodesic and shear-free, and that the spacetime possesses a distinguished vector field that is simultaneously a Killing vector of the full spacetime and the flat background, but need not be timelike with respect to the background metric. We show that the gauge field obtained by contracting this distinguished Killing vector with the Kerr-Schild graviton solves the vacuum Maxwell equations, and that this definition of the Kerr-Schild double copy implies the Weyl double copy when the spacetime is Petrov type D. When the Killing vector is taken to be timelike with respect to the background metric, we recover the familiar Kerr-Schild double copy, but the prescription is well defined for any vacuum Kerr-Schild spacetime and we present new examples where the Killing vector is null or spacelike. While most examples of physical interest are type D, vacuum Kerr-Schild spacetimes are generically of Petrov type II. We present a straightforwardmore » example of such a spacetime and study its double copy structure. Our results apply to real Lorentzian spacetimes as well as complex spacetimes and real spacetimes with Kleinian signature, and provide a simple correspondence between real and self-dual vacuum Kerr-Schild spacetimes. This correspondence allows us to study the double copy structure of a self-dual analog of the Kerr spacetime. We provide evidence that this spacetime may be diffeomorphic to the self-dual Taub-NUT solution.« less

Authors:
 [1];  [2];  [2];  [3]
+ Show Author Affiliations
  1. Arizona State Univ., Tempe, AZ (United States)
  2. Brown Univ., Providence, RI (United States)
  3. Arizona State Univ., Tempe, AZ (United States); Brown Univ., Providence, RI (United States)
Publication Date:
Research Org.:
Arizona State Univ., Tempe, AZ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
2281897
Grant/Contract Number:  
SC0019470
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: 2023; Journal Issue: 9; Journal ID: ISSN 1029-8479
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Black holes; Gauge-gravity correspondence; Space-time symmetries

Citation Formats

Easson, Damien A., Herczeg, Gabriel, Manton, Tucker, and Pezzelle, Max. Isometries and the double copy. United States: N. p., 2023. Web. doi:10.1007/jhep09(2023)162.
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Easson, Damien A., Herczeg, Gabriel, Manton, Tucker, & Pezzelle, Max. Isometries and the double copy. United States. https://doi.org/10.1007/jhep09(2023)162
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Easson, Damien A., Herczeg, Gabriel, Manton, Tucker, and Pezzelle, Max. Mon . "Isometries and the double copy". United States. https://doi.org/10.1007/jhep09(2023)162. https://www.osti.gov/servlets/purl/2281897.
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@article{osti_2281897,
title = {Isometries and the double copy},
author = {Easson, Damien A. and Herczeg, Gabriel and Manton, Tucker and Pezzelle, Max},
abstractNote = {In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell’s equations. However, it is well known that the vacuum Einstein equations imply that the Kerr-Schild vector is geodesic and shear-free, and that the spacetime possesses a distinguished vector field that is simultaneously a Killing vector of the full spacetime and the flat background, but need not be timelike with respect to the background metric. We show that the gauge field obtained by contracting this distinguished Killing vector with the Kerr-Schild graviton solves the vacuum Maxwell equations, and that this definition of the Kerr-Schild double copy implies the Weyl double copy when the spacetime is Petrov type D. When the Killing vector is taken to be timelike with respect to the background metric, we recover the familiar Kerr-Schild double copy, but the prescription is well defined for any vacuum Kerr-Schild spacetime and we present new examples where the Killing vector is null or spacelike. While most examples of physical interest are type D, vacuum Kerr-Schild spacetimes are generically of Petrov type II. We present a straightforward example of such a spacetime and study its double copy structure. Our results apply to real Lorentzian spacetimes as well as complex spacetimes and real spacetimes with Kleinian signature, and provide a simple correspondence between real and self-dual vacuum Kerr-Schild spacetimes. This correspondence allows us to study the double copy structure of a self-dual analog of the Kerr spacetime. We provide evidence that this spacetime may be diffeomorphic to the self-dual Taub-NUT solution.},
doi = {10.1007/jhep09(2023)162},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2023,
place = {United States},
year = {Mon Sep 25 00:00:00 EDT 2023},
month = {Mon Sep 25 00:00:00 EDT 2023}
}
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