General Relativity predicts the existence of relativistic corrections to the static Newtonian potential which can be calculated and verified experimentally.

The existence of a universal long distance quantum correction to the Newtonian potential should be relevant for a wide class of gravity theories.

Logarithmic potential, Newtonian potential, balayage, inverse balayage, linear optimization, duality, Chebychev constant, extremal problem.

and, for each (finite Borel-) measure [mu], define the logarithmic or Newtonian potential by

Furthermore, from astrophysics one knows that spiral galaxies do not follow Newtonian potential exactly.

Meanwhile it is known, that General Relativity is strictly related to Newtonian potential (Poisson's equation).

Furthermore, one cannot assign the value of the constant appearing in the Schwarzschild lineelement to the

Newtonian potential in the infinitely far field because Schwarzschild space is asymptotically Minkowski space, not asymptotically Special Relativity and not asymptotically Newtonian dynamics.

Below in order to compare we can write down the same equations for the spin components in the case of the

Newtonian potential.

2] by means of a comparision with the

Newtonian potential, but this identification is rather dubious.

When H, V, E' represents gravitational Planck constant,

Newtonian potential, and the energy per unit mass of the orbiting body, respectively, and [3]:

It also can be shown that Finsler-Berwald-Moor metric is equivalent with pseudo-Riemannian metric, and an expression of

Newtonian potential can be found for this metric [2a].

There gravity is described by the

Newtonian potential energy field [PHI](r, t), such that g = -[nabla][PHI], and we have for a "free-falling" quantum system, with mass m,