Observational Constraints on the Completeness of Space near
  Astrophysical Objects
  We consider the observational effects of a deficit angle, w, in the topology
of the solar system and in the 'double pulsar' system PSR J0737-3039A/B. Using
observations of the perihelion precession of Mercury, and the gravitational
deflection of light due to the Sun, we constrain the magnitude of such a
deficit angle in the solar system to be 2*pi*(1-w), with 0<(1-w)<10^(-9) at 95%
confidence. We calculate the effects of a deficit angle on the periastron
advance, geodetic precession rate and inclination angle of the double pulsar
system and use the observational data to obtain the constraint
0<(1-w)<2.4*10^(-8) at 95% confidence. Although this result is weaker than the
solar system bound, it is in a very different physical environment, where
accumulating data is likely to lead to tighter constraints in the future.
