A hole in a distribution of negative mass produces a positive gravitational lensing effect.
Qualitatively this equivalent to the effect due to an homogeneous sphere of positive mass. See figure 13
...Classically one use the gravitational lensing to evaluate the so-called invisible mass contained in a galaxy. People uses to say : "the dark matter exists in our galaxy : we measure it, through the missing mass effect". In this twin cosmological model a strong lensing effect should not be a proof of the existence of invisble mass in a galaxy, but could be due to the action of the invisible surrounding antipodal matter, which could be evaluated from the measured effects. See the figure 14.
...In
our galaxy the mass necessary to prevent the explosion by centrifugal force
is about 10 times higher that the observed mass. If the confinement effect
is due to the action of surrounding invisible antipodal matter, it means that
the effect of this invisible matter is important. This could be general in
the region of the universe we live in. Then all the neigbour galaxies could
be surronded by dense halos of antipodal matter, and the observed gravitational
lensing should be mostly due to the antipodal material than to the galaxies
themselves.
...
...The model based on the equation (1) gives a new insight on the missing mass problem [1] and on the very large structure of the Universe. This work was based on the low field and weak velocities hypothesis and refered to a quasi-steady Universe, at cosmologic scale, with respect to space and time.In order to complete this cosmological model we have now to study the evolution of the Universe as a whole.