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:
“Among all the world’s races, some obscure Bedouin tribes possibly apart, Americans are the most prone to misinformation. This is not the consequence of any special preference for mendacity, although at the higher levels of their public administration that tendency is impressive. It is rather that so much of what they themselves believe is wrong.”
—John Kenneth Galbraith (b. 1908)
“Is it true or false that Belfast is north of London? That the galaxy is the shape of a fried egg? That Beethoven was a drunkard? That Wellington won the battle of Waterloo? There are various degrees and dimensions of success in making statements: the statements fit the facts always more or less loosely, in different ways on different occasions for different intents and purposes.”
—J.L. (John Langshaw)