Huygens' Principle  

In General
$ Def: (Hadamard's point of view) A wave equation satisfies Huygens' principle if the support of its Green function with no incoming waves, or fundamental solution, the one with source (x) (t), is entirely contained on the future or past light cone of that point.
* Idea: Roughly, data concentrated in a small region at time t' will only produce a disturbance on a sphere of radius c(t–t') (without leaving tails behind); The value of a massless field at a point in spacetime is determined by data on the intersection of its past light cone with some spacelike surface.
* Flat space: It holds for massless Klein-Gordon particles in even d > 2.

Related Concepts > see Hadamard's Conjecture; perturbations in general relativity; velocity [speedup in random media]; wave equations.

References
@ General: Künzle PCPS(68); Günther 88; Bombelli, Couch & Torrence JMP(91); Soodak & Tiersten AJP(93)may; Bombelli & Sonego JPA(94)mp/00; Liu mp/03 ["proof"].
@ Electromagnetism: Kaiser a0906 [distributional approach].
@ Other fields: Noonan CQG(95) [higher-rank]; Baum JGP(97) [Dirac]; Berest & Loutsenko CMP(97) [KdV solitons].
@ Variations: Luís EJP(07) [complementary version, in terms of Wigner functions and rays].

In Curved Spacetime > s.a. phenomenology of gravity.
* General results: A necessary condition is that (M, g) be an Einstein space.
* Ricci-flat spacetime: For 2 = 0, the only cases are Minkowski space and plane waves.
@ General references: McLenaghan PCPS(68); Goldoni JMP(77); Sonego & Faraoni JMP(92); Noonan CQG(96) [necessary condition, Bach tensor = 0].
@ Specific types of spacetimes: Noonan CQG(95) [conformally flat], CQG(01) [scalar, Einstein spacetime]; McLenaghan & Sasse AIHP(96)mp/05 [Petrov III, electromagnetism and Dirac]; Anderson et al AIHP(99)mp/05 [Petrov III, scalar]; Czapor et al AIHP(99)mp/05 [Petrov III, conformally invariant scalar].
> Specific theories: see metric perturbations in general relativity; wave phenomena.

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