Direct Detection of Universal Expansion by Holonomy in the McVittie
  Spacetime
  In general relativity the parallel transfer of a vector around a closed curve
in spacetime, or along two curves which together form a closed loop, usually
results in a nonzero deficit angle between the vector's initial and final
positions. We show that such holonomy in the McVittie spacetime, which
represents a gravitating object imbedded in an expanding universe, can in
principle be used to directly detect the expansion of the universe, for example
by measuring changes in the components of a gyroscopic spin axis. Although such
changes are of course small, they are large enough (\D S \sim 10^{-7}) that
they could conceivably be measured if the real universe behaved like the
McVittie spacetime. The real problem is that virialization will lead to domains
decoupled from the global expansion on a scale much larger than that of the
solar system, making such an experiment infeasible probably even in principle.
Nevertheless the effect is of interest in relation to ongoing discussions,
dating back at least to Einstein and Straus, which concern the relationship
between the expansion of the universe and local systems.
