The structure and properties of asymptotically shear-free NGCs (our main topic) are best understood by first looking at the special case of congruences that are shear-free everywhere (except at their caustics). Though shear-free congruences are also found in algebraically-special spacetimes, in this section only the shear-free NGCs in Minkowski spacetime, , are discussed [7]

3.1 The flat-space good-cut equation and good-cut functions

3.2 Real cuts from the complex good cuts, I

3.3 Approximations

3.4 Asymptotically-vanishing Maxwell fields

3.4.1 A prelude

3.4.2 Asymptotically-vanishing Maxwell fields: General properties

3.4.3 A coordinate and tetrad system attached to a shear-free NGC

3.4.4 Complex Liénard–Wiechert Maxwell field

3.4.5 Asymptotically vanishing Maxwell fields & shear-free NGCs

The (non-)uniqueness of spherical harmonic expansions

3.4.6 The complex center of charge

3.2 Real cuts from the complex good cuts, I

3.3 Approximations

3.4 Asymptotically-vanishing Maxwell fields

3.4.1 A prelude

3.4.2 Asymptotically-vanishing Maxwell fields: General properties

3.4.3 A coordinate and tetrad system attached to a shear-free NGC

3.4.4 Complex Liénard–Wiechert Maxwell field

3.4.5 Asymptotically vanishing Maxwell fields & shear-free NGCs

The (non-)uniqueness of spherical harmonic expansions

3.4.6 The complex center of charge

Living Rev. Relativity 15, (2012), 1
http://www.livingreviews.org/lrr-2012-1 |
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