Re: Parallel Transport Of A Vector Around a Closed Curve in Schwarschild Metric

From: Neil (neil_delver_at_yawwho.com)
Date: 02/18/05 

Date: Fri, 18 Feb 2005 17:44:42 +0000 (UTC)

"David Park" <djmp@earthlink.net> wrote in message
news:95vQd.1740$9J5.1735@newsread2.news.atl.earthlink.net...
> <lost.and.lonely.physicist@gmail.com> wrote in message
> news:1108430326.236765.302190@c13g2000cwb.googlegroups.com...
> > I understand there is an experiment floating in space right now testing
> > the Lens-Thirring effect (Gravity B probe).
> >
> > Am I correct, however, that even if the Earth is not rotating a vector
> > parallel-transported around a closed curve around the Earth would not
> > necessarily be returned to the same vector?
<<snip>>
> > Is this a sensible result? I had earlier thought that vectors do not
> > return to their original condition only for a spining Earth, hence the
> > term "frame dragging".
> >
>
> Yes, there is an effect called the 'geodetic precession' that is unrelated
> to, and much greater than, the frame dragging effect. It's about 6.61 arc
> seconds per year for Gravity Probe B.
>
> This is discussed in the Hartle Gravitation text in Chapter 14. However the
> result is a little different than what you give.
>
> dphi(geodetic) = 2 Pi [1 - Sqrt(1- 3M/R)] per orbit where geometric units
> are used.
>
> There is also an analysis in the Foster & Nightingale text: A Short Course
> in General Relativity in Section 4.7, where they call it the 'geodesic
> effect'.
>
> I think the effect is principally caused because the satellite makes one
> orbit in coordinate time t, but the tracking of the gyroscopes is in proper
> time tau.
>
...
How is angular momentum conserved?