Petrov Classification - Generalization To Higher Dimensions

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 were as twinned lambs that did frisk i’ the sun
    And bleat the one at th’ other. What we changed
    Was innocence for innocence; we knew not
    The doctrine of ill-doing, nor dreamed
    That any did. Had we pursued that life,
    And our weak spirits ne’er been higher reared
    With stronger blood, we should have answered heaven
    Boldly “Not guilty,” the imposition cleared
    Hereditary ours.
    William Shakespeare (1564–1616)

    Why is it that many contemporary male thinkers, especially men of color, repudiate the imperialist legacy of Columbus but affirm dimensions of that legacy by their refusal to repudiate patriarchy?
    bell hooks (b. c. 1955)