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:
“We live between two worlds; we soar in the atmosphere; we creep upon the soil; we have the aspirations of creators and the propensities of quadrupeds. There can be but one explanation of this fact. We are passing from the animal into a higher form, and the drama of this planet is in its second act.”
—W. Winwood Reade (1838–1875)
“Words are finite organs of the infinite mind. They cannot cover the dimensions of what is in truth. They break, chop, and impoverish it.”
—Ralph Waldo Emerson (1803–1882)