Computer Science
Scientific paper
Feb 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998gregr..30..227b&link_type=abstract
General Relativity and Gravitation, Volume 30, Issue 2, pp.227-238
Computer Science
3
Bel-Robinson Tensor, Factorizations, Principal Null Directions, Gravitational Energy
Scientific paper
Recently Bonilla and Senovilla studied factorizations of the symmetric and tracefree rank four Bel-Robinson tensor Tabcd into two symmetric tracefree rank two tensors. While the Bel-Robinson tensor has the dimension of energy density squared, each of these factors has the dimension of energy density. When the two factors can be chosen to be equal they are called the "square root" of Tabcd. The approach used was purely tensorial. In this paper we use spinors and show that the factors can be found in a very simple way using the principal null directions of the Weyl tensor. We obtain a factorization of the Weyl spinor into two symmetric rank two spinors, which when multiplied by their complex conjugates give the tracefree and symmetric factors of Tabcd. The factorization is immediately seen to be non-unique in most cases and the number of essentially non-equivalent factorizations becomes clear. It also becomes obvious that the square root only can exist in spacetimes of Petrov types N, D and O, in which cases one can equally well speak about the "square root" of the Weyl spinor. Explicit formulas for the factors of the Weyl spinor are given for all Petrov types.
No associations
LandOfFree
Spinor Factorizations of the Bel-Robinson Tensor does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Spinor Factorizations of the Bel-Robinson Tensor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spinor Factorizations of the Bel-Robinson Tensor will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1225597