Does [Huygens' principle](http://en.wikipedia.org/wiki/Huygens%E2%80%93Fresnel_principle) hold in even dimensional (2m+1,1) curved spacetimes, or are there certain necessary conditions for it to hold? In other words, if I have Cauchy data for a field satisfying the wave equation on curved space, does the field value at a point only depend on the intersection of the past light cone with the Cauchy surface?

In addition, what are the physical implications in cases when Huygens' principle fails, both in odd dimensional flat space and curved spacetimes? Are there complications with the Cauchy problem or notable physical phenomena other than wave tails? I would be interested in implications for electromagnetic and gravitational radiation.