3 Shear-Free NGCs in Minkowski Space

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, 𝕄, are discussed [7Jump To The Next Citation Point]

 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

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