Maxwell fields and shear-free null geodesic congruences

Newman, Ezra T.

doi:10.1088/0264-9381/21/13/007

Cited by 36 publications

(65 citation statements)

References 24 publications

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“…In section 2.3, we describe the requirements which must be satisfied by a gauge field single copy of a Kerr-Schild metric. Referring to previous work of Newman, in section 3 we relate these single copies to real slices of complex Liénard-Wiechert fields [13], and use this identification to systematically construct all four-dimensional black hole spacetimes on Minkowski backgrounds. In section 4, we present a test for Kerr-Schild structure in any number of dimensions.…”

Section: Contentsmentioning

confidence: 99%

“…In fact, any field strength with this property is a Liénard-Wiechert field. The result of [13] is to generalize this construction to twisting congruences. If we take a complex extension of Minkowski space and consider a particle on a worldline z µ (τ ) = x µ (τ ) + iy µ (τ ), (3.3) gives a complex gauge field which can be used to construct a complex field strength.…”

Section: Liénard-wiechert Single Copy Fieldsmentioning

confidence: 99%

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Kerr-Schild double copy and complex worldlines

Bah

Dempsey

Weck

2020

J. High Energ. Phys.

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We use the classical double copy to identify a necessary condition for a gauge theory source to constitute a single copy of a solution to Einstein's equations. In the case of four-dimensional Kerr-Schild spacetimes on Minkowski backgrounds, we extend this condition to a parameterization of the corresponding single copies. These are given by Liénard-Wiechert fields of charges on complex worldlines. This unifies the known instances of the double copy black holes on flat four-dimensional backgrounds into a single framework. Furthermore, we use the more generic condition identified to show why the black ring in five dimensions does not admit Kerr-Schild coordinates.

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Section: Contentsmentioning

confidence: 99%

Section: Liénard-wiechert Single Copy Fieldsmentioning

confidence: 99%

Kerr-Schild double copy and complex worldlines

Bah

Dempsey

Weck

2020

J. High Energ. Phys.

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“…, by omitting cubic terms including L 2 φ 0 2 , then using the first two terms of the Taylor series 16) and the Clebsch-Gordon expansions of the products of the spherical harmonics (see Appendix A) we finally have (after simplification) for just the l = 1 harmonic terms…”

Section: The Quantities Qηmentioning

confidence: 99%

“…The simple answer is that an (analytic) asymptotically flat Maxwell field in Minkowski space with non-vanishing total charge generates, in the complex Minkowski space, a unique complex analytic world-line: the complex center of charge world-line, where the real part describes the standard center of charge while the ribbon thickness encodes magnetic dipole information [16,17]. For the case of asymptotically flat space-times there are two situations: the vacuum asymptotically flat and the Einstein-Maxwell asymptotically flat spacetimes.…”

Section: Introductionmentioning

confidence: 99%

Light cones in relativity: Real, complex, and virtual, with applications

Adamo

Newman

2011

Phys. Rev. D

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We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and asymptotically flat settings, complexified future null infinity, I + C , acts as a "holographic screen," interpolating between two dual descriptions of the null geodesic congruence. One description constructs a complex null geodesic congruence in a complex space-time whose source is a complex worldline; a virtual source as viewed from the holographic screen. This complex null geodesic congruence intersects the real asymptotic boundary when its source lies on a particular open-string type structure in the complex space-time. The other description constructs a real, twisting, shear-free or asymptotically shear-free null geodesic congruence in the real space-time, whose source (at least in Minkowski space) is in general a closed-string structure: the caustic set of the congruence. Finally we show that virtually all of the interior space-time physical quantities that are identified at null infinty I + , (center of mass, spin, angular momentum, linear momentum, force) are given kinematic meaning and dynamical descriptions in terms of the complex world-line.

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“…Though we are dealing with real electromagnetic fields in real Minkowski space, this trivial observation can be formally generalized [8,9,17] to complex translations defining a complex center of charge world-line around which both the electric and magnetic dipoles vanish. Associated with this complex center of charge world-line is a null geodesic congruence in Minkowski space that is shear-free but twisting.…”

Section: Introductionmentioning

confidence: 99%

On the physical interpretation of asymptotically flat gravitational fields

2008

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A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space-times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy-momentum and the energy-momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein-Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found.

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Maxwell fields and shear-free null geodesic congruences

Cited by 36 publications

References 24 publications

Kerr-Schild double copy and complex worldlines

Kerr-Schild double copy and complex worldlines

Light cones in relativity: Real, complex, and virtual, with applications

On the physical interpretation of asymptotically flat gravitational fields

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