Taub-NUT from the Dirac monopole

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.

Section: Basicsmentioning

confidence: 75%

The classical double copy of a point charge

Kim

Lee

Monteiro

et al. 2020

“…In standard setups, this integral must vanish since the null normals provide a trivialization of the normal bundle. However, notable exceptions are given by configurations possessing nontrivial NUT charges, where C 1 is seen to be proportional to the NUT charge (see, for example, the analysis near null infinity in Bondi coordinates of [90]). In order for the surface S to be a regular embedded spacelike surface when the NUT charge is nonvanishing, there must be a physical Misner string penetrating the surface, which provides a compensating contribution to the outer curvature, to enforce that the normal bundle remains globally trivial [91][92][93][94].…”

Section: Nontrivial Bundles and Nut Chargesmentioning

confidence: 99%

Gravitational edge modes, coadjoint orbits, and hydrodynamics

Donnelly

Freidel

Moosavian

et al. 2021

The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is conjectured to be an important aspect of quantum gravity. As a step towards quantization, we derive a complete classification of the positive-area coadjoint orbits of this group for boundaries that are topologically a 2-sphere. This classification parallels Wigner’s famous classification of representations of the Poincaré group since both groups have the structure of a semidirect product. We find that the total area is a Casimir of the algebra, analogous to mass in the Poincaré group. A further infinite family of Casimirs can be constructed from the curvature of the normal bundle of the boundary surface. These arise as invariants of the little group, which is the group of area-preserving diffeomorphisms, and are the analogues of spin. Additionally, we show that the symmetry group of hydrodynamics appears as a reduction of the corner symmetries of general relativity. Coadjoint orbits of both groups are classified by the same set of invariants, and, in the case of the hydrodynamical group, the invariants are interpreted as the generalized enstrophies of the fluid.

“…In (31), the time evolution equation of A 1 involves the coupling constant a. Since A 1 is related to the electric dipole [39], the non-minimal coupling effect can be seen from the first radiating source in the multipole expansion.…”

Section: Solution Space In Series Expansionmentioning

confidence: 99%

“…The rest three supplementary equations determine the time evolution of the integration constants M, N and q. Since those integration constants are related to the conserved quantities, the supplementary equations are also called conservation equations [31].…”

Section: Conservation Laws and The Loss Of Massmentioning

confidence: 99%

“…In recent years, physics near null infinity has obtained renewed interest from several aspects, e.g. holography [2][3][4][5][6], asymptotic symmetries [7][8][9][10][11][12], infrared physics [13][14][15][16][17][18][19][20][21][22], memory effect [23][24][25], and gravitational conserved quantities [26][27][28][29][30][31]. The Bondi gauge plays a central role in all the relevant research.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic structure of Einstein-Maxwell-dilaton theory and its five dimensional origin

Lü¹,

Mao²,

Wu³

2019

We consider Einstein-Maxwell-dilaton theory in four dimensions including the Kaluza-Klein theory and obtain the general asymptotic solutions in Bondi gauge. We find that there are three different types of news functions representing gravitational, electromagnetic, and scalar radiations. The mass density at any angle of the system can only decrease whenever there is any type of news function. The solution space of the Kaluza-Klein theory is also lifted to five dimensions. We also compute the asymptotic symmetries in both four dimensional Einstein-Maxwell-dilaton theory and five dimensional pure Einstein theory. We find that the symmetry algebras of the two theories are the same.