Very-long-baseline radio interferometry (VLBI) of quasars grazing the solar limb…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Schwarzschild spacetime and the tests of general relativity · Schwarzschild spacetime and the tests of general relativity

The Geometry of Gravity, Ch Solar-system tests, the PPN framework and alternative theories

Problem

Very-long-baseline radio interferometry (VLBI) of quasars grazing the solar limb measures the coefficient of the light-deflection formula to be

\dfrac{1+\gamma_{\rm PPN}}{2} = 1.0000060 \pm 0.0000100

(a stated result for this problem). ((a)) Starting from the parametrised deflection formula

\Delta\phi = \dfrac{1+\gamma_{\rm PPN}}{2}\cdot\dfrac{4GM_\odot}{bc^2}

, obtained by redoing the null-geodesic calculation with

\gamma_{\rm PPN}

multiplying the spatial part of the PPN metric, explain why dividing the measured

\Delta\phi

by the independently known

4GM_\odot/bc^2

isolates

(1+\gamma_{\rm PPN})/2

. ((b)) Find

\gamma_{\rm PPN}-1

with its

1\sigma

uncertainty from the stated VLBI result. ((c)) Brans-Dicke theory predicts

\gamma_{\rm PPN} = \dfrac{1+\omega_{\rm BD}}{2+\omega_{\rm BD}}

. Using twice the

1\sigma

uncertainty from part (b) as the two-standard-deviation bound on

|\gamma_{\rm PPN}-1|

, derive a lower bound on the Brans-Dicke coupling constant

\omega_{\rm BD}

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