Black holes are singularities. This means that they must exist as point masses, according to general relativity. The gravitational field around a point mass must have a hyperbolic potential profile, not a parabolic one as assumed by Newton’s Law of Gravity. This is because the event horizon of a black-hole is not a true surface like that of a planet or a surface zone like that of a star. The only characteristic of a black-hole that makes any difference here is the point-mass at the Heisenberg uncertainty constrained center. Mordechai Milgrom's work (see below) proves that there is more to a black-hole than just its event horizon.

A hyperbola is characterized by asymptotes that define the extreme behavior of the curve far from the origin. Hyperbolic curves merely approach, but never reach the asymptotes. Proper parabolas, on the other hand, approach and reach their extreme values eventually. For instance, a proper parabola will actually pass through the origin, but the equivalent hyperbola never will.

The hyperbolic gravitational field profile (a 2D graph) around a black hole has significant consequences. These effects include a much slower fall-off of the gravitational potential as one proceeds to larger distances, r, from the origin. The mass of the supermassive black hole at the center of most spiral galaxies is a few million solar masses at most. But, the mass of the entire galaxy is several hundred billion solar masses. So, it would seem that the mass of the central black hole is insignificant relative to the galaxy as a whole. But, since the gravitational fields of the black hole and of the galaxy must be perfectly aligned and co-axial, the fields must superpose, reinforce and merge as one. So, the effective mass of the central black hole must be in the hundreds of billions of solar masses. The consequence of this is that the gravitational field experienced by any given star or group of stars near the periphery of a spiral galaxy must be declining as 1/r*, by the definition of a hyperbola, not as 1/r^{2}, according to Newton’s Law. The unit vector,, allows proper dimensional analysis. It is a constant, so the equation, say, F = GmM/ r*, is hyperbolic in nature. The symbol, r*, is the variable r (distance from the graphical origin or from the center of a galaxy) multiplied by the dimensioned value of the unit vector associated with the vector equivalent of r, (rr). This ensures that the "hyperbolic" Newtonian equation F = GmM/r* passes dimensional analysis. But, there are other fundamental justifications for its use. Normally we use the "parabolic" form F = GmM/r_{1}^{2}. But not when super-massive black holes are involved.

This explains the MOND effect, the residual gravitational potential constant that was observed by Mordehai Milgrom in 1983 for stars near the peripheries of spiral galaxies. MOND stands for Modified Newtonian dynamics, a proposed revision of Newton’s Law. I call it the “MOND effect” to distinguish it from MOND itself because when the hyperbolic (proportional to 1/r*) gravitational field is considered, no modification of Newton’s Law is required. Instead, a footnote must be appended to acknowledge that a hyperbolic 1/r* field can exist around black holes.

Another consequence is that there is no need to hypothesized “Dark Matter”. The rotational distribution effects around galaxies and the behavior of galactic clusters and super-clusters is explained by the hyperbolic black hole gravitational field effect. The behavior of colliding galaxies having hyperbolic gravitational fields that are in the process of merging is also explained.

Since the hypothesis of the existence of a huge point mass called an “inflaton” is used to explain numerous characteristics of the cosmic microwave background radiation (CMB) and the expansion of the universe, it makes sense to consider that the universe was once immersed in a hyperbolic 1/r* gravitational field. The inflaton itself can be said to have existed before the Big Bang (BB). So, its hyperbolic gravitational field must have existed then too.

The question arises: What happened to the hyperbolic field after the BB? At the instant of the BB, the hyperbolic field must have begun to collapse or transition from a hyperbolic field to a parabolic Newtonian filed. This transition should still be occurring, the process requiring the entire lifetime of the universe to complete. The hyperbolic field is inherently more intense than the equivalent parabolic field, so the transition to the weaker field must be releasing potential energy. This energy will show up as kinetic energy in the form of the accelerating expansion rate of the universe.

So, the source of “Dark Energy” is gravitational, not due to a new type of field called "quintessence". It would give a positive cosmological constant, Lambda, in the Friedmann equations under the FLRW metric. These are relativistic treatments, but the hyperbolic 1/r* gravitational field equations are purely Newtonian. Nevertheless, no “quintessence” field is needed, just as no “Dark Matter” is needed to explain the MOND effect.