Generalization To Higher Dimensions
A. Coley, R. Milson, V. Pravda and A. Pravdová (2004) developed a generalization of algebraic classification to arbitrary spacetime dimension . Their approach uses a null frame basis approach, that is a frame basis containing two null vectors and, along with spacelike vectors. Frame basis components of the Weyl tensor are classified by their transformation properties under local Lorentz boosts. If particular Weyl components vanish, then and/or are said to be Weyl-Aligned Null Directions (WANDs). In four dimensions, is a WAND if and only if it is a principal null direction in the sense defined above. This approach gives a natural higher-dimensional extension of each of the various algebraic types II,D etc. defined above.
An alternative, but inequivalent, generalization was previously defined by de Smet (2002), based on a spinorial approach. However, the de Smet is restricted to 5 dimensions only.
Read more about this topic: Petrov Classification
Famous quotes containing the words higher and/or dimensions:
“This might be the end of the world. If Joe lost we were back in slavery and beyond help. It would all be true, the accusations that we were lower types of human beings. Only a little higher than apes. True that we were stupid and ugly and lazy and dirty and, unlucky and worst of all, that God Himself hated us and ordained us to be hewers of wood and drawers of water, forever and ever, world without end.”
—Maya Angelou (b. 1928)
“The truth is that a Pigmy and a Patagonian, a Mouse and a Mammoth, derive their dimensions from the same nutritive juices.... [A]ll the manna of heaven would never raise the Mouse to the bulk of the Mammoth.”
—Thomas Jefferson (1743–1826)