On certain global conformal invariants and 3-surface twistors of initial data sets

Details On certain global conformal invariants and 3-surface twistors of initial data sets On certain global conformal invariants and 3-surface twistors of initial data sets

1999-09-16

arxiv.org/abs/gr-qc/9909052v1

Class.Quant.Grav. 17 (2000) 793-811

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, Plain TEX

Scientific paper

10.1088/0264-9381/17/4/305

The Chern-Simons functionals built from various connections determined by the initial data $h_{\mu\nu}$, $\chi_{\mu\nu}$ on a 3-manifold $\Sigma$ are investigated. First it is shown that for asymptotically flat data sets the logarithmic fall-off for $h_{\mu\nu}$ and $r\chi_{\mu\nu}$ is the necessary and sufficient condition of the existence of these functionals. The functional $Y_{k,l}$, built in the vector bundle corresponding to the irreducible representation of SL(2,C) labelled by (k,l), is shown to be determined by the Ashtekar-Chern-Simons functional and its complex conjugate. $Y_{k,l}$ is conformally invariant precisely in the l=k (i.e. tensor) representations. An unexpected connection with twistor theory is found: $Y_{k,k}$ can be written as the Chern-Simons functional built from the 3-surface twistor connection, and the not identically vanishing spinor parts of the 3-surface twistor curvature are given by the variational derivatives of $Y_{k,k}$ with respect to $h_{\mu\nu}$ and $\chi_{\mu\nu}$. The time derivative $\dot Y_{k,k}$ of $Y_{k,k}$ is another conformal invariant of the initial data set, and for vanishing $\dot Y_{k,k}$, in particular for all Petrov III and N spacetimes, the Chern-Simons functional is a conformal invariant of the whole spacetime.

Affiliated with

Also associated with

No associations

Rating

On certain global conformal invariants and 3-surface twistors of initial data sets 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 On certain global conformal invariants and 3-surface twistors of initial data sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On certain global conformal invariants and 3-surface twistors of initial data sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-712412