Spinor-helicity and the algebraic classification of higher-dimensional spacetimes

Monteiro, Ricardo; Nicholson, Isobel; O’Connell, Donal

doi:10.1088/1361-6382/ab03df

Cited by 23 publications

(29 citation statements)

References 86 publications

(251 reference statements)

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“…It should also be possible to extend the vacuum Weyl double copy [15], and a higher-dimensional version based on [77], to include the dilaton and B-field, using ideas from double field theory. In fact, this could potentially elucidate some aspects of the generalised curvatures of double field theory, alluded to in the appendix.…”

Section: Resultsmentioning

confidence: 99%

The classical double copy of a point charge

Kim

Lee

Monteiro

et al. 2020

J. High Energ. Phys.

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The classical double copy relates solutions to the equations of motion in gauge theory and in gravity. In this paper, we present two double-copy formalisms for relating the Coulomb solution in gauge theory to the two-parameter Janis-Newman-Winicour solution in gravity. The latter is a static, spherically symmetric, asymptotically flat solution that generically includes a dilaton field, but also admits the Schwarzschild solution as a special case. We first present the classical double copy as a perturbative construction, similar to its formulation for scattering amplitudes, and then present it as an exact map, with a novel generalisation of the Kerr-Schild double copy motivated by double field theory. The latter formalism exhibits the relation between the Kerr-Schild classical double copy and the string theory origin of the double copy for scattering amplitudes.

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Section: Resultsmentioning

confidence: 99%

The classical double copy of a point charge

Kim

Lee

Monteiro

et al. 2020

J. High Energ. Phys.

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“…A sophisticated extension of the Weyl double copy would include non-type D spacetimes. Another natural direction is the application to higher-dimensional solutions, which motivated the recent paper [65] extending to higher dimensions the spinorial approach to general relativity.…”

Section: Discussionmentioning

confidence: 99%

Type D spacetimes and the Weyl double copy

Luna

Monteiro

Nicholson

et al. 2019

Class. Quantum Grav.

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153

262

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We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important solutions. We present a double copy of curvatures that applies to all spacetimes of this type -the Weyl double copy -relating the curvature of the spacetime to an electromagnetic field strength. We show that the Weyl double copy is consistent with the previously known Kerr-Schild double copy, and in fact resolves certain ambiguities of the latter. The most interesting new example of the classical double copy presented here is that of the C-metric. This well-known solution, which represents a pair of uniformly accelerated black holes, is mapped to the Liénard-Wiechert potential for a pair of uniformly accelerated charges. We also present a new double-copy interpretation of the Eguchi-Hanson instanton. arXiv:1810.08183v2 [hep-th] 1 Apr 2019 -1 -an antisymmetric tensor. The focus of this article will be on the double copy in classical field theory. Moreover, we will restrict to pure Einstein gravity, so that the dilaton and the antisymmetric tensor are not present; we will comment on these fields in section 6.The KLT relations have the advantage that an underlying reason for the relation between gauge theory and gravity is clear: by joining two open strings, you get one closed string. But they have the disadvantage that the relations themselves become quite complicated for high multiplicity. More recently, Bern, Carrasco and Johansson (BCJ) discovered a new and simple form for the double copy [2] which also leads to a natural formulation of the double copy at loop level [3]. This form of the double copy has been extensively studied at tree level, leading to various proofs [4][5][6][7][8][9][10][11][12][13][14][15][16]. At loop level, the double copy has been extensively studied [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], but to date it is still a conjecture [27]. Nevertheless, the BCJ double copy is a powerful tool in the theory of scattering amplitudes, which has led to rich new insights into the structure of supergravity, e.g. [32][33][34][35][36][37][38][39][40]. A celebrated recent example is the detailed computation of the UV structure of maximal supergravity at five loops [41]. The double copy is reviewed in, for example, [42][43][44].The success of the double copy for scattering amplitudes motivated the investigation of its manifestation for solutions of the classical field equations, with early steps given in [45][46][47]. Since the principles of the double copy, as currently understood, are perturbative in nature, it is remarkable that exact relations between solutions can be found, as discovered in [48]. In the same way that solutions to the Maxwell equations provide a class of linear solutions to the Yang-Mills equations (with trivial colour dependence), there is a class of solutions that linearise the Einstein equations. Kerr-Schild metrics belong to this class, and so do certain multi-Kerr-Sch...

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“…We have studied the Weyl tensor here but there will also be spinor analogues of our formulae in each dimension (cf. [111]).…”

Section: Discussionmentioning

confidence: 99%

“…Turning to the Weyl-NP scalars, the classification of spacetimes in general dimensions via properties of the Weyl tensor has been discussed by Coley, Milson, Pravda and Pravdova (CMPP) in [107,108] (see also [109,110]). More recently, the relationship between these classifications has been discussed and compared to a spinor-based analysis in [111], who show that in five dimensions the CMPP and spinor approaches are equivalent. The classification of Maxwell fields is also described there.…”

Section: Jhep09(2020)127mentioning

confidence: 99%

Weyl doubling

Alawadhi

Berman

Spence

2020

J. High Energ. Phys.

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We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space. We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions. For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordström metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.

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Spinor-helicity and the algebraic classification of higher-dimensional spacetimes

Cited by 23 publications

References 86 publications

The classical double copy of a point charge

The classical double copy of a point charge

Type D spacetimes and the Weyl double copy

Weyl doubling

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