Gravity Probe B and GEM

11 Dec 2009

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Fri, 12/11/2009 - 07:18

doug

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Joined: 03/13/2009

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Hello:

I was curious if the predictions for the gravity probe B experiment would be different for general relativity versus GEM. The two metrics are identical to first order PPN accuracy. These effects are will be looked at at first order, so the predictions should be identical. A key equation from 'Gravitation and Spacetime' by Ohanian and Ruffini relates spin to the Christoffel symbol:
$\frac{\partial S^k}{\partial \tau} = - \Gamma^k_{\alpha \beta} S^{\alpha} \frac{\partial x^{\beta}}{\partial \tau}\quad eq.~149, ~p~416$
Analysis of this term averaged over a complete rotation leads to the geodetic or de Sitter precession. Since this uses the connection and not the Riemann curvature tensor, I think it should be exact agreement between general relativity and GEM.

The other effect is a spin-spin interaction, the Lense-Thirring precession. The book handles this issue to briefly for me to tell if there might be a difference.