General relativity predicts that normal mass (positive mass) results in the curvature of spacetime which in return leads to gravitation. Since space and time are bonded together, any change on the fabric of space may inevitably lead to a change in time, as postulated by Einstein's theory of relativity. So the effect of positive mass on time is that it slows it down through the formulation of an attractive gravitational field, but what happens to time in the presence of negative mass?
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The time dilation factor with respect to an observer at infinity is
$$\sqrt{1-\frac{\text{2 G M}}{\text{c}^2\text{ r}}}$$
so if we plug in G=1, c=1, r=10 and M=+1 we get the clocks running slower by a factor of 0.8944 if they are in a distance of 10GM/c² from the center of the positive mass.
If we change the sign of M to M=-1 we get a time dilation factor of 1.095 so mathematically the clocks should run faster near negative masses than they would for a field free observer.
Yukterez
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The arrow of time is believed to be related to the fact that the universe started in a state of low entropy and is evolving towards a state of larger entropy. The effect of negative mass will not change this. The reason is that any model of negative mass will leave the initial state of the universe as as state of low entropy. A rather uniform distribution of mass in the presence of gravity, be it either attractive or negative, will still constitute a state of low entropy, whereas states of high entropy will be created as mass clumps start to form either as an effect of positive or negative mass. The second law of thermodynamics is a statistical theorem that can be derived from very general principles, without the details of the force fields, thus there nothing a priori that would make a negative mass to reverse the arrow of time.