On Complex Structures in Physics

Trautman, Andrzej

doi:10.1007/978-1-4612-1422-9_34

Cited by 13 publications

(14 citation statements)

References 19 publications

(47 reference statements)

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“…This may introduce a new insight into general relativity, where the three-dimensional CR structures correspond [37,39,40] to congruences of shear-free and null geodesics in spacetimes 8 . In particular, the shear-free congruence of null geodesics associated with the celebrated Kerr spacetime can be interpreted in terms of a certain class of point equivalent second-order ODEs.…”

Section: Realification Of a Three-dimensional Cr Structurementioning

confidence: 99%

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Three-dimensional Cauchy–Riemann structures and second-order ordinary differential equations

Nurowski

Sparling

2003

Class. Quantum Grav.

107

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The equivalence problem for second-order ordinary differential equations (ODEs) given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate three-dimensional Cauchy-Riemann structures. This approach enables an analogue of the Fefferman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second-order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs.

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Section: Realification Of a Three-dimensional Cr Structurementioning

confidence: 99%

“…Here we focus on properties of Fefferman metrics associated with equations (40). It is known [22] that the Fefferman metrics associated with the three-dimensional CR structures admitting three symmetries of Bianchi type corresponding to n = −3 satisfy the Bach equations.…”

Section: Realification Of a Three-dimensional Cr Structurementioning

confidence: 99%

Three-dimensional Cauchy–Riemann structures and second-order ordinary differential equations

Nurowski

Sparling

2003

Class. Quantum Grav.

107

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“…It has been found that there exists a close relation between the Cauchy-Riemann structure on a 4-dimensional Riemannian manifold and the Goldberg-Sachs theorem [26,27]. It has been found that there exists a close relation between the Cauchy-Riemann structure on a 4-dimensional Riemannian manifold and the Goldberg-Sachs theorem [26,27].…”

Section: By Maciej Przanowskimentioning

confidence: 97%

Editorial note to: J. N. Goldberg and R. K. Sachs, A theorem on Petrov types

Krasiński

Przanowski

2008

Gen Relativ Gravit

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Assumptions about properties of congruences of curves in a spacetime have powerful implications for the Weyl tensor. A well-known example is the conclusion that follows from the propagation equations of kinematical tensors in relativistic hydrodynamics [1]: If, in a perfect fluid spacetime, there exists a family of timelike curves with zero shear, rotation and acceleration, then the spacetime must be conformally flat. The theorem proven in the paper reprinted here is another example, where limitations imposed on the Weyl tensor by properties of congruences of null curves are discussed. Namely, a geodesic and shearfree null congruence exists in a vacuum spacetime if and only if its Weyl tensor is algebraically special. The congruence is then the degenerate principal null congruence of the Weyl tensor. (The theorem is further extended to include electromagnetic field with geodesic rays and a null field.)The republication of the original paper can be found via

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“…Passing to the inhomogeneous domain by linearity will turn out this null higher-degree electromagnetic field into a self dual or an anti-self dual one. The definition of = √−1 is ambiguous here but since it exists at least if the Hodge map defines a complex structure on ΓΛ ( ) which is always possible for some [24].…”

Section: B Adding Closed Conformal Killing-yano Forms To Killing-yano Formsmentioning

confidence: 99%

On a Relation Between Twistors and Killing Spinors

Açık

2018

Cumhuriyet Science Journal

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Inspiring from the consequence of constructing conformal Killing-Yano forms out of Killing-Yano forms and closed conformal Killing-Yano forms, this work includes a method for building up twistors from Killing spinors which can be analogously interpreted as the quantum electrodynamical pair annihilation process in background gravitational fields. The former consequence is easily verified if one introduces a new defining differential equation for (possibly inhomogeneous) Killing-Yano forms which is free from auxiliary vector fields, as is done in this text. From this point of view a neat relation between the symmetry operators of massive and massless Dirac equation is also introduced. Some other physical interpretations are also included.

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On Complex Structures in Physics

Cited by 13 publications

References 19 publications

Three-dimensional Cauchy–Riemann structures and second-order ordinary differential equations

Three-dimensional Cauchy–Riemann structures and second-order ordinary differential equations

Editorial note to: J. N. Goldberg and R. K. Sachs, A theorem on Petrov types

On a Relation Between Twistors and Killing Spinors

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