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Originally Posted by DaveRFinn
Since this increase in distance applies to any pair of masses on opposite sides of the new black hole the effect of the formation of the black hole would appear to be a slight reduction in the average density of the universe. For any particle, in calculating the gravitational effect of mass on the far side of the hole, the bigger the black hole the larger the area of sky affected by the black hole and the greater the reduction in density.
Is this analysis correct? If not, why not?
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No, it's not. The amount of space isn't increasing. It's just the length of the path through the universe is longer. Think of it this way. If your standing in the middle of a straight road running north and south. The shortest path to something north of you is to move north, straight down the middle of the road. If you move east and west of the middle of the road, as your move to the north, the street isn't getting bigger (it stays the same size), but the path has become longer than the straight down the middle path.