Is it possible that black holes generate space? Suppose that there is a limit to the strength of a gravitational field. Then, if the mass is added to a black hole, the gravity term in the EFE will not increase, so the spatial expansion term must increase in order to balance the mass-energy term. That is exactly as cosmic inflation is presumed to work, except that this spatial expansion is local. As long as the spatial expansion evens out in time, this is not in contradiction of any observations, is it?
Spatial expansion due to black holes neatly accounts for the galactic rotation anomaly, because it allows for space to be denser - in other words, distances we observe optically are smaller than the physical distances - nearer the galactic core, and lower in the outer regions. According to the Gaussian formulation of gravity, the gravitational aceleration and hence the rotation speed will remain constant with increasing radius if the physical area of the surface of a sphere centered on the galactic center remains constant with increasing radius. This is possible if the speed at which new space distributes itself is appropriate.
 A: You are saying "in other words, distances we observe optically are smaller than the physical distances - nearer the galactic core, and lower in the outer regions.".
Now you mean that the distances we observe optically are smaller then the physical distance nearer the galactic core? Do you mean that the optically observed distance, that is, the path that light would take, is shorter then the physical distance, that is, the distance in plain 3D?
According to GR, it is the opposite what happens near a black hole. The distance that light takes near a black hole is measured (from far away) longer then what we would measure in plain 3D (straight). This together with the fact that the time passes slower near a black hole (measured from far away) creates the Shapiro effect (it is actually for the Sun).
So you should mean that the distances near the galactic center are longer then what we would measure in plain 3D (straight) due to the effects of gravity. But according to our currently accepted theories, the SM and GR, this does not mean that extra space is created, we usually use the expression "space is bent".


The galaxy rotation problem is the discrepancy between observed galaxy rotation curves and the theoretical prediction, assuming a centrally dominated mass associated with the observed luminous material. When mass profiles of galaxies are calculated from the distribution of stars in spirals and mass-to-light ratios in the stellar disks, they do not match with the masses derived from the observed rotation curves and the law of gravity. A solution to this conundrum is to hypothesize the existence of dark matter and to assume its distribution from the galaxy's center out to its halo.


You are saying that the spatial expansion that you suggest that is created by black holes in the galaxy accounts for the rotational anomaly. In other words, the rotational anomaly means that the outer parts of the galaxy are rotating too fast. Now you suggest that this is because the distances inside the galaxy are shorter then observed. But this would mean the opposite, because if distances near the galaxy center are shorter, this would cause the observed speed of stars near the center to be faster not slower.
